Old Math 205 Exams
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Text sections denoted (Lay) refer to the third edition of Linear Algebra and its Applications by Lay.
Text sections denoted (Strang) refer to the third edition of Introduction to Linear Algebra by Strang.
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Term 
Date 
Instructor 
Topic(s) 
Text Sections 
Solutions 
W14 
Ross 
(Exam 1) systems of linear equations, row reduction, echelon forms, solutions of systems, use of calculators to find RREF, analyzing solutions, linear combination and span of a set of vectors, homogeneous systems and particular solutions, conditions under which a vector b is in the span of the columns of a matrix A, matrix equations, linear independence  (Lay) 1.11.7  
W14 
Ross 
(Exam 2) basis for null and row space of a matrix, basis for abstract vector spaces, subspaces, linear transformations on abstract spaces, elementary matrices  (Lay) 4.14.3  
F13 
Buell 
systems of linear equations and their solutions, linear independence, linear transformations, matrix operations  (Lay) 1.11.5, 1.71.9, 2.1  
F13 
Buell 
IMT, determinants, vector spaces, subspaces, column space, null space, basis, rank, changeofbasis, eigenvalues, eigenvectors, diagonalization  (Lay) 2.22.3, 3.1, 4.14.6, 5.15.3  
F13 
Buell 
IMT, determinants, vector spaces, subspaces, column space, null space, basis, rank, changeofbasis, eigenvalues, eigenvectors, diagonalization  (Lay) 2.22.3, 3.1, 4.14.6, 5.15.3  
F11 
Buell 
Final: all from 10/07 and 11/18 exams plus inner products, length, orthogonality, orthogonal sets and projections, least squares, diagonalization  (Lay) 1.11.5, 1.71.9, 2.12.3, 3.13.2, 4.14.6, 5.15.3, 6.16.3, 6.5, 7.1 
no 

W13 
Wong 
systems of linear equations and their solutions, linear independence, linear transformations, matrix operations and matrix inverses  (Lay) 1.11.5, 1.71.9, 2.12.3  no 

W13 
Wong 
determinants, vector spaces, subspaces, column space, null space, basis, rank, eigenvectors, eigenvalues, characteristic equation, diagonalization, linear transformations  (Lay) 3.13.2, 4.14.6, 5.15.4  
W13 
Wong 
Final: all from 02/06 and 03/18 exams plus inner product, orthogonality, GramSchmidt process, diagonalization  (Lay) 1.11.5, 1.71.9, 2.12.3, 3.13.2, 4.14.6, 5.15.4, 6.16.4, 7.1  no 

F12 
Ross 
(Exam 1) systems of linear equations, row reduction, echelon forms, solutions of systems, use of calculators to find RREF, analyzing solutions, linear combination and span of a set of vectors, homogeneous systems and particular solutions, conditions under which a vector b is in the span of the columns of a matrix A, matrix equations, linear independence, linear transformations, an application to economics (exchange model)  (Lay) 1.11.9  
F12 
Ross 
(Exam 2) Leontief input/output model, basis, column space, null space, determinants, eigenvectors, eigenvalues, characteristic polynomial, eigenspace, diagonalization  (Lay) 2.6, 2.82.9; 3.13.2, 5.15.3  
F12 
Ross 
(Final Exam) all from 10/05 and 11/09 exams plus plus basis for null and row space, abstract vector spaces, change of basis, inner products, orthogonal sets and projections, leastsquares problems and their applications  (Lay) 1.11.9, 2.12.3, 2.6, 2.82.9; 3.13.2, 4.14.3, 4.54.7, 5.15.3, 6.16.3, 6.56.6  
W12 
Webster 
systems of linear equations and their solutions, linear independence, linear transformations, matrix operations and matrix inverses, subspace, dimension, rank, determinants  (Lay) 1.11.9, 2.12.3, 2.82.9, 3.13.2  no 

W12 
Webster 
eigenvectors, eigenvalues, characterisitic equation, diagonalization, linear transformations, inner products, orthogonal sets and projections, GramSchmidt, leastsquares problems, linear models, abstract vector spaces  (Lay) 5.15.4, 6.16.6  no 

W12 
Webster 
Final: all from 02/27 and 03/23 exams plus inner product spaces and their applications, diagonalization of symmetric matrices, quadratic forms  (Lay) 1.11.9, 2.12.3, 2.82.9, 3.13.2, 5.15.4, 6.16.8, 7.17.2  no 

F11 
Buell 
systems of linear equations and their solutions, linear independence, linear transformations, matrix operations  (Lay) 1.11.5, 1.71.9, 2.1  
F11 
Buell 
IMT, determinants, vector spaces, subspaces, column space, null space, basis, rank, changeofbasis, eigenvalues, eigenvectors, diagonalization (review sheet is here)  (Lay) 2.22.3, 3.1, 4.14.6, 5.15.3  
F11 
Buell 
Final: all from 10/10 and 11/18 exams plus inner products, length, orthogonality, orthogonal sets and projections, least squares, diagonalization  (Lay) 1.11.5, 1.71.9, 2.12.3, 3.13.2, 4.14.6, 5.15.3, 6.16.3, 6.5, 7.1 
no 

W11 
Jayawant 
systems of linear equations and their solutions, linear independence, linear transformations, matrix operations and matrix inverses  (Lay) 1.11.5, 1.6 (pages 6062), 1.71.9, 2.12.3 (page 129)  
W11 
Jayawant 
subspace, column space, null space, bases, dimension, rank, determinants, eigenvalues, eigenvectors, characteristic equation, diagonalization, inner product, length, orthogonality  (Lay) 2.82.9, 3.13.2, 5.15.3, 6.1  
F10 
Webster 
systems of linear equations and their solutions, linear independence, linear transformations, matrix operations and matrix inverses, subspace, dimension, rank, determinants  (Lay) 1.11.9, 2.12.3, 2.82.9, 3.13.2  no 

F10 
Webster 
eigenvectors, eigenvalues, characterisitic equation, diagonalization, linear transformations, inner products, orthogonal sets and projections, GramSchmidt, leastsquares problems, linear models, abstract vector spaces  (Lay) 5.15.4, 6.16.6  no 

F10 
Webster 
Final: all from 10/15 and 11/19 exams plus inner product spaces and their applications, diagonalization of symmetric matrices, quadratic forms  (Lay) 1.11.9, 2.12.3, 2.82.9, 3.13.2, 5.15.4, 6.16.8, 7.17.2  no 

W10 
Jayawant 
systems of linear equations and their solutions, linear independence, linear transformations, matrix operations and matrix inverses, subspace  (Lay) 1.11.9, 2.12.3, 2.8 (subspace definition only)1.1  
W10 
Jayawant 
subspace, column space, null space, bases, dimension, rank, determinants, eigenvalues, eigenvectors, characteristic equation, diagonalization, inner product, length, orthogonality  (Lay) 2.82.9, 3.13.2, 5.15.3, 6.1  
W10 
Jayawant 
Final: all from 02/12 and 03/19 exams plus vector spaces, orthogonal sets, orthogonal projections, least squares  (Lay) 1.11.9, 2.12.3, 2.82.9, 3.13.2, 4.14.6, 5.15.3, 6.16.3, 6.56.6  
W10 
Ross 
(Exam 1) systems of linear equations, row reduction, echelon forms, solutions of systems, use of calculators to find RREF, analyzing solutions, linear combination and span of a set of vectors, homogeneous systems and particular solutions, conditions under which a vector b is in the span of the columns of a matrix A, matrix equations, linear independence, linear transformations (onetoone/onto/matrix of, etc)  (Lay) 1.11.5, 1.71.9 1.1  
W10 
Ross 
(Exam 2) exchange models (econ application), invertible matrices, basis for column spaces, characteristic polynomial, eigenvalues/vectors/spaces, diagonalization, subspaces, determinants  (Lay) 1.6, 2.12.3, 2.9, 3.13.2, 5.15.31.1  
W10 
Ross 
(Final Exam) all from 02/12 and 03/19 exams plus basis for null and row space, abstract vector spaces, change of basis, inner products, orthogonal sets and projections, leastsquares problems and their applications 
(Lay) 1.11.9, 2.12.3, 2.82.9, 3.13.2, 4.14.3, 4.54.7, 5.15.3, 6.16.3, 6.56.6  
F09 
Jayawant 
systems of linear equations and their solutions, linear independence, linear transformations, matrix operations and matrix inverses  (Lay) 1.11.9, 2.12.3 1.1  
F09 
Jayawant 
subspace, column space, null space, bases, dimension, rank, determinants, eigenvalues, eigenvectors, characteristic equation, diagonalization, inner product, length, orthogonality, orthogonal sets  (Lay) 2.82.9, 3.13.2, 5.15.3, 6.16.2(pages 384389 only)1.1  
F09 
Jayawant 
Final: all from 10/09 and 11/13 exams plus vector spaces, orthogonal projections, least squares  (Lay) 1.11.9, 2.12.3, 2.82.9, 3.13.2, 4.14.6, 5.15.3, 6.16.3, 6.56.6, 7.1  
F09 
Ross 
(Exam 1) systems of linear equations, row reduction, echelon forms, solutions of systems, use of calculators to find RREF, analyzing solutions, linear combination and span of a set of vectors, homogeneous systems and particular solutions, conditions under which a vector b is in the span of the columns of a matrix A, matrix equations, linear independence, linear transformations; an application to economics (exchange tables)  (Lay) 1.11.9  
F09 
Ross 
(Exam 2) invertible matrices, column & null spaces, characteristic polynomial, eigenvalues/vectors/spaces, diagonalization, subspaces, determinants  (Lay) 2.12.3, 2.9, 3.13.2, 5.15.3  
F09 
Ross 
(Final Exam) all from 10/09 and 11/13 exams plus general vector spaces, change of basis, inner products, orthogonal sets and projections, leastsquares problems and their applications 
(Lay) 1.11.9, 2.12.3, 2.9, 3.13.2, 4.14.3, 4.54.7, 5.15.3, 6.16.3, 6.56.6  
W09 
Jayawant 
systems of linear equations and their solutions, linear independence, linear transformations, matrix operations and matrix inverses, subspace, column space, null space  (Lay) 1.11.9, 2.12.3, 2.8 1.1  
W09 
Jayawant 
null space, bases, dimension, rank, determinants, eigenvalues, eigenvectors, characteristic equation, diagonalization, inner product, length, orthogonality, orthogonal sets  (Lay) 2.82.9, 3.13.2, 5.15.3, 6.16.2 1.1  
W09 
Jayawant 
Final: all from 02/13 and 03/20 exams plus vector spaces, orthogonal projections, least squares, diagonalization  (Lay) 1.11.9, 2.12.3, 2.82.9, 3.13.2, 4.14.6, 5.15.3, 6.16.3, 6.56.6, 7.1 1.1  
W09 
Ross 
review problems for Exam 1  (Lay) 1.11.5, 1.71.9, 2.12.3 1.1  
W09 
Ross 
(Exam 1) systems of linear equations, row reduction, echelon forms, solutions of systems, use of calculators to find RREF, analyzing solutions, linear combination and span of a set of vectors, homogeneous systems and particular solutions, conditions under which a vector b is in the span of the columns of a matrix A, matrix equations, linear independence, linear transformations, matrix multiplication, inverses, elementary matrices, equivalent statements about invertible matrices  (Lay) 1.11.5, 1.71.8, 2.12.3  
W09 
Ross 
(Exam 2) exchange models, column & null spaces, characteristic polynomial, eigenvalues/vectors/spaces, diagonalization, subspaces, determinants  (Lay) 1.6, 2.8, 3.13.2, 5.15.3  
W09 
Ross 
(Final Exam) all from 02/13 and 03/20 exams plus general vector spaces, change of basis, inner products, orthogonal sets and projections, leastsquares problems and their applications  (Lay) 1.11.8, 2.12.3, 2.8, 3.13.2, 4.14.7, 5.15.3, 6.16.3, 6.56.6  
F08 
Ross 
(Exam 1) systems of linear equations, row reduction, echelon forms, solutions of systems, use of calculators to find RREF, analyzing solutions, linear combination and span of a set of vectors, homogeneous systems and particular solutions, conditions under which a vector b is in the span of the columns of a matrix A, matrix equations, linear independence, linear transformations  (Lay) 1.11.5, 1.71.8  
F08 
Ross 
(Exam 2) linear transformations: onetoone and onto; matrix multiplication, matrix inverse and usage; vector spaces in general; subspaces; exchange models; null and column spaces; linear independence, spanning and basis; dimension, rank  (Lay) 1.6, 2.12.2, 4.14.3, 4.54.6  
W08 
Greer 
systems of linear equations and their solutions, linear independence, linear transformations, linear models and applications  (Lay) 1.11.10  
W08 
Greer 
matrix operations, inverses of matrices, applications, vector spaces, null space, column space, linear tranformations, bases, dimension, rank, eigenvectors, eigenvalues, characteristic equation, diagonalization  (Lay) 2.12.3, 2.7, 4.14.6, 5.15.3  
W08 
Greer 
Final: all from 02/05 and 03/20 exams plus inner products, orthogonal sets, orthogonal projections, least squares, linear models  (Lay) 1.11.10, 2.12.3, 2.7, 4.14.6, 5.15.3, 6.16.3, 6.56.6  
W08 
Ross 
(Exam 1) systems of linear equations, row reduction, echelon forms, solutions of systems, use of calculators to find RREF, analyzing solutions, linear combination and span of a set of vectors, homogeneous systems and particular solutions, conditions under which a vector b is in the span of the columns of a matrix A, matrix equations, linear independence  (Lay) 1.11.5, 1.7  yess 

W08 
Ross 
(Exam 2) linear transformations, onetoone, onto; matrix multiplication, matrix inverse and usage; definition of, finding, using and properties of determinants; vector spaces in general; subspaces; exchange models  (Lay) 1.61.8, 2.12.3, 3.13.2, 4.1  yess 

W08 
Ross 
(Final Exam) all from 02/01 and 03/07 exams plus null, column, row spaces, dimension, rank, eigenvectors, eigenvalues, characteristic polynomial, diagonalization, inner products, orthogonal sets and projections, leastsquares problems and their applications, and the Leontief inputoutput model  (Lay) 1.11.8, 2.12.3, 2.6, 3.13.2, 4.14.3, 4.54.6, 5.15.3, 6.16.3, 6.56.6  yess 

F07 
Ross 
(Exam 1) systems of linear equations and their augmented matrices, echelon forms, vector equations, matrix equations, solutions in terms of particular solutions, solutions of the homogeneous system, linear independence, linear transformations  (Lay) 1.11.5, 1.71.8  
F07 
Ross 
(Exam 2) matrix multiplication, inverses and their uses, elementary matrices, LUfactorizations, determinants, abstract vector spaces, subspaces, null and column space, dimension  (Lay) 2.12.3, 2.5, 313.2, 4.14.3  
F07 
Ross 
(Final Exam) all from 10/05 and 11/09 exams plus rank, bases, eigenvectors, eigenvalues, diagonalization, inner products, lengths of vectors, orthogonal sets, orthogonal projections, leastsquares problems, applications of 6.5 topics  (Lay) 1.11.5, 1.71.8, 2.12.3, 2.5, 313.2, 4.14.3, 4.6, 5.1, 5.3, 6.16.3, 6.56.6  
W07 
Greer 
systems of linear equations and their solutions, linear independence, linear transformations, linear models and applications, matrix operations and matrix inverses  (Lay) 1.11.10, 2.12.2  
W07 
Greer 
invertible matrices, computer graphics, subspaces, dimension, rank, determinants, Markov chains, eigenvectors, eigenvalues, characteristic equation, diagonalization, discrete dynamical systems, inner product, orthogonality, orthogonal sets  (Lay) 2.3, 2.72.9, 3.13.2, 4.9, 5.15.3, 5.6, 6.16.2  
W07 
Greer 
Final: all from 02/09 and 03/23 exams plus orthogonal projections, least squares, linear models, diagonalization, quadratic forms  (Lay) 1.11.10, 2.12.3, 2.72.9, 3.13.2, 4.9, 5.15.3, 5.6, 6.16.3, 6.56.6, 7.17.2  
F06 
Jayawant 
systems of linear equations and their solutions, linear independence, linear transformations, matrix operations and matrix inverses, subspace, column space, row space  (Lay) 1.11.5, 1.71.9, 2.12.3, 2.8  
F06 
Jayawant 
null space, bases, dimension, rank, determinants, eigenvalues, eigenvectors, characteristic equation, diagonalization, inner product, length, orthogonality, orthogonal sets  (Lay) 2.82.9, 3.13.2, 5.15.3, 6.16.2  
F06 
Jayawant 
Final: all from 10/06 and 11/10 exams plus vector spaces, orthogonal projections, least squares, diagonalization, quadratic forms  (Lay) 1.11.5, 1.71.9, 2.12.3, 2.82.9, 3.13.2, 4.14.6, 5.15.3, 6.16.3, 6.5, 7.17.2  
W06 
Shor 
systems of linear equestions and their solutions, linear independence, linear transformations, matrix operations and matrix inverses  (Lay) 1.11.5, 1.71.9, 2.12.2  
W06 
Shor 
inverses, determinants, vector spaces, null space, column space, bases, linear independence, dimension, rank, eigenvectors, eigenvalues  (Lay) 2.3, 3.13.2, 4.14.6, 5.1  
W06 
Shor 
Final: all from 02/03 and 03/08 exams plus characteristic equation, diagonalization, inner product, orthogonality, least squares, quadratic forms  (Lay) 1.11.5, 1.71.9, 2.12.3, 3.13.2, 4.14.6, 5.15.3, 6.16.5, 7.17.2  
F05 
Jayawant 
systems of linear equations and their solutions, free variables, linear independence, spanning sets, linear transformations, matrices and their inverses  (Lay) 1.11.5, 1.71.9, 2.12.3  
F05 
Jayawant 
subspaces, dimension, rank, determinants, eigenvalues, eigenvectors, characteristic equation, diagonalization, linear transformations  (Lay) 2.82.9, 3.13.2, 5.15.4  
F05 
Jayawant 
Final: all from 10/07 and 11/11 exams plus vector spaces, null space, column space, bases, dimension, rank, inner product, orthogonality, leastsquares, diagonalization  (Lay) 1.11.5, 1.71.9, 2.12.3, 2.82.9, 3.13.2, 4.14.6, 5.15.4, 6.16.3, 6.5, 7.1  
F05 
Ross 
(Exam 1) systems of linear equations and their solutions, free variables, linear independence, spanning sets  (Lay) 1.11.5, 1.7  
F05 
Ross 
(Exam 2) linear transformations
from R^n to R^m (one to one, onto, compositions, matrices of), matrix operations, inverses, elementary matrices, and review of Exam I material 
(Lay) 1.11.5, 1.71.9, 2.12.3  
F05 
Ross 
(Exam 3) determinants, abstract vector spaces, subspaces, null & column space, kernel & image of a linear transformation, linear independence, span, basis, dimension, rank  (Lay) 3.13.2, 4.14.3, 4.54.6  
F05 
Ross 
(Final Exam) all from 10/07 and 11/09 exams plus eigenvectors, eigenvalues, diagonalization, dot products, orthogonal sets, row space, orthogonal projections, leastsquares problems and applications  (Lay) 1.11.5, 1.71.9, 2.12.3, 3.13.2, 4.14.3, 4.54.6, 5.15.3, 6.16.3, 6.56.6  no 

W05 
Jayawant 
systems of linear equations and their solutions, linear independence, linear transformations  (Lay) 1.11.5, 1.7, 1.8  
W05 
Jayawant 
matrix algebra, determinants, vector spaces and subspaces  (Lay) 2.12.3, 2.5, 3.13.2, 4.1  
W05 
Jayawant 
null space, column space, linear transformations, coordinate systems, bases, dimension, rank, eigenvectors, eigenvalues, characteristic equations  (Lay) 4.24.6, 5.15.2  
W05 
Jayawant 
Final: all from 01/28, 02/18, and 03/18 exams plus diagonalization, orthogonality and least squares, and quadratic forms  (Lay) 1.11.5, 1.7, 1.8, 2.12.3, 3.1, 3.2, 4.14.6, 5.15.3, 6.16.3, 7.1, 7.2  
W05 
Ross 
(Exam 1) systems of linear equations and their solutions, linear independence  (Lay) 1.11.5, 1.7  no 

W05 
Ross 
(Exam 2) matrix algebra, determinants  (Lay) 2.12.3, 2.5, 3.13.2  no 

W05 
Ross 
(Exam 3) vector space, subspace, null space, column space, linear transformations, bases, dimension, rank  (Lay) 4.14.3, 4.54.6  no 

W05 
Ross 
(Final Exam) all from 01/28, 02/18, and 03/18 exams plus eigenvectors, eigenvalues, characteristic polynomial, diagonalization, inner product, length, orthogonality, orthogonal sets, orthogonal projections, least squares problems and their applications  (Lay) 1.11.5, 1.7, 2.12.3, 2.5, 3.13.2, 4.14.3, 4.54.6, 5.15.3, 6.16.3, 6.5, 6.6  no 

F04 
Haines 
systems of linear equations and their solutions, linear independence, linear transformations, applications  (Lay) 1.11.10  no 

F04 
Haines 
matrix algebra, determinants  (Lay) 2.12.9, 3.13.3  no 

F04 
Haines 
vector spaces, eigenvalues and eigenvectors  (Lay) 4.14.7, 4.9, 5.15.6  no 

F04 
Haines 
Final: all from 09/27, 10/27, and 12/01 exams plus orthogonality, diagonalization, and quadratic forms  (Lay) 1.11.10, 2.12.9, 3.13.3, 4.14.7, 4.9, 5.15.6, 6.16.3, 7.17.2  no 

W04 
Greer 
systems of linear equations and their solutions, linear independence, linear transformations, vectors, matrix operations  (Lay) 1.11.5, 1.7, 1.8, 2.1  
W04 
Greer 
inverse matrices, matrix factorization, determinants, vector spaces, subspaces, null space, column space, linear transformations  (Lay) 2.22.5, 3.13.2, 4.14.2  
W04 
Greer 
bases, dimension, rank, eigenvectors, eigenvalues, diagonalization, inner product  (Lay) 4.34.6, 5.15.4, 6.1  
W04 
Greer 
Final: all from 02/04, 03/03, and 03/24 plus orthogonality, least squares, inner product spaces, diagonalization, quadratic forms  (Lay) 1.11.5, 1.71.8, 2.12.5, 3.13.2, 4.14.6, 5.15.4, 6.16.3, 6.5, 6.7, 7.17.2  
W04 
Ross 
(Exam 1) systems of linear equations and their solutions, linear independence, linear transformations, vectors (Note: cover page contains important information.)  (Lay) 1.11.5, 1.71.8  no 

W04 
Ross 
(Exam 2) matrix operations, inverse matrices, matrix factorization, determinants, vector spaces, subspaces, null space, column space, linear transformations  (Lay) 2.12.3, 2.5, 3.13.2, 4.14.2  no 

W04 
Ross 
(Exam 3) bases, dimension, rank, change of basis, eigenvectors, eigenvalues, diagonalization  (Lay) 4.34.7, 5.15.4  no 

W04 
Ross 
(Final Exam) all from 02/06, 03/05, and 03/26 exams plus orthogonality, least squares, applications to linear models  (Lay) 1.11.5, 1.71.8, 2.12.3, 2.5, 3.13.2, 4.14.7, 6.16.3, 6.56.6  no 

F03 
Johnson 
vectors, solving linear equations  (Strang) Chapters 1 and 2  
F03 
Johnson 
vector spaces and subspaces, orthogonality  (Strang) Chapters 3 and 4  
F03 
Johnson 
Final: all from 10/06 and 11/14 exams plus determinants, eigenvalues, and eigenvectors  (Strang) Chapters 15, 6.1, 6.2, 6.4  no 

F02 
Johnson 
vectors, solving linear equations  (Strang) Chapters 1 and 2  
F02 
Johnson 
vector spaces and subspaces, orthogonality  (Strang) Chapters 3 and 4  
F02 
Johnson 
Final: all from 10/07 and 11/15 exams plus determinants, eigenvalues, and eigenvectors  (Strang) Chapters 15, 6.1, 6.2, 6.4  no 

W02 
Johnson 
vectors, solving linear equations  (Strang) Chapters 1 and 2  
W02 
Johnson 
vector spaces and subspaces, orthogonality  (Strang) Chapters 3 and 4  
W02 
Johnson 
Final: all from 02/15 and 03/22 exams plus determinants, eigenvalues, and eigenvectors  (Strang) Chapters 15, 6.1, 6.2, 6.4  no 

F01 
Johnson 
vectors, solving linear equations  (Strang) Chapters 1 and 2  
F01 
Johnson 
vector spaces and subspaces, orthogonality  (Strang) Chapters 3 and 4  
F01 
Johnson 
Final: all from 10/08 and 11/16 exams plus determinants, eigenvalues, and eigenvectors  (Strang) Chapters 15, 6.1, 6.2, 6.4  no 