Old Math 205 Quizzes
Click on the date of each quiz in order to view it. If a solution set is available, you may click on it at the far right.
Text sections refer to the third edition of Linear Algebra and its Applications by Lay.
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Term 
Date 
Instructor 
Topic(s) 
Text Sections 
Solutions 
F15 
Wong 
systems of linear equations, row reduction and echelon forms  1.1, 1.2  
F15 
Wong 
vector equations, matrix equations, solution sets of linear systems  1.3, 1.4, 1.5  
F15 
Wong 
linear independence, linear transformations and their matrices  1.7, 1.8, 1.9  
F15 
Wong 
matrix operations, inverse of a matrix, invertible matrices  2.1, 2.2, 2.3  
W15 
Ross 
(Quiz 1, version 1) systems of equations, matrix representation, reduced row echelon form, vector equations, linear combination, span of a set of vectors  1.1, 1.2, 1.3  
W15 
Ross 
(Quiz 1, version 2) systems of equations, matrix representation, reduced row echelon form, vector equations, linear combination, span of a set of vectors  1.1, 1.2, 1.3  
W15 
Ross 
(Quiz 2, version 1) conditions for consistency, solutions of matrix equations in parametric vector form  1.4, 1.5  
W15 
Ross 
(Quiz 2, version 2) conditions for consistency, solutions of matrix equations in parametric vector form  1.4, 1.5  
W15 
Ross 
(Quiz 3) linear transformations  1.8, 1.9  
W15 
Ross 
(Quiz 4) matrix algebra: multiplication, inverse, transpose  2.1, 2.2  
W15 
Ross 
(Quiz 5) abstract vector spaces and subspaces  4.1  
W15 
Ross 
(Quiz 6) change of basis matrix, eigenvectors, eigenvalues  4.7, 5.1  
W15 
Ross 
(Quiz 7) eigenvectors, eigenvalues, eigenspaces, characteristic polynomials  5.1, 5.2  
W15 
Ross 
(Quiz 8) diagonalization, inner (dot) product  5.3, 6.1  
W14 
Ross 
(Quiz 1) using the RREF of a matrix to solve a system of linear equations  1.1, 1.2  
W14 
Ross 
(Quiz 2) vector equation, linear combination, span of a set of vectors  1.3  
W14 
Ross 
(Quiz 3) linear independence of column vectors, definition of linear transformation  1.7, 1.8  
W14 
Ross 
(Quiz 4) matrix multiplication, inverse of a 2x2 matrix, onetoone and onto linear transformations  1.9, 2.1, 2.2  
W14 
Ross 
(Quiz 5) abstract vector spaces and subspaces, linear independence and linear combinations in such spaces  4.1, 4.3  
W14 
Ross 
(Quiz 6) change of basis, determinants by cofactors, eigenvalues, eigenvectors, characteristic polynomials  3.1, 4.7, 5.1, 5.2  
W14 
Ross 
(Quiz 7) diagonalization, dot (inner) products, unit vectors, perpendicular vectors, distance between vectors  5.3, 6.1  
F13 
Buell 
reduced row echelon form, span of vectors  1.1, 1.2, 1.3  
F13 
Buell 
solutions to Ax=b in parametric vector form, solution sets to linear systems, linear independence  1.4, 1.5, 1.7  
F13 
Buell 
linear tranformations, the matrix of a linear transformation, definitions  1.8, 1.9  
F13 
Buell 
matrix multiplication, inverse of a matrix  2.1, 2.2  
F13 
Buell 
vector space, subspace, null space, column space, basis  4.1, 4.2, 4.3  
F13 
Buell 
coordinate systems, dimension  4.4, 4.5  
F13 
Buell 
determinants, rank  3.1, 4.6  
F13 
Buell 
eigenvectors, eigenvalues, characteristic equation, diagonalization  5.1, 5.2, 5.3  
F13 
Buell 
inner product, length, orthogonality  6.1, 6.2  
W13 
Wong 
systems of linear equations, row reduction and echelon forms  1.1, 1.2  
W13 
Wong 
vector equations, matrix equations  1.3, 1.4  
W13 
Wong 
solution sets to linear systems, linear independence  1.5, 1.7  
W13 
Wong 
linear transformations, matrix of a linear transformation  1.8, 1.9  
W13 
Wong 
determinants and their properties  3.1, 3.2  
W13 
Wong 
vector spaces, linear transformations  4.1, 4.2  
W13 
Wong 
coordinate vectors, bases  4.3, 4.4  
W13 
Wong 
eigenvalues, eigenvectors, eigenspace  5.1  
W13 
Wong 
orthogonal sets, projection, length  6.1, 6.2  
W13 
Wong 
GramSchmidt process, QR decomposition  6.3, 6.4  
F12 
Ross 
(Quiz 1) using RREF of an augmented matrix to solve a system of equations, span of a set of column vectors  1.1, 1.2, 1.3, 1.4  
F12 
Ross 
(Quiz 2) solutions to Ax=b in parametric vector form, equilibrium model application from economics  1.5, 1.6  
F12 
Ross 
(Quiz 3) relationships among vectors in linearly dependent sets  1.7  
F12 
Ross 
(Quiz 4) matrix multiplication  2.1  
F12 
Ross 
(Quiz 5) Leontief InputOutput model, finding a basis for the column space of a matrix  2.6, 2.8  
F12 
Ross 
(Quiz 6) determinants  3.1, 3.2  
F11 
Buell 
reduced row echelon form, span of vectors  1.1, 1.2, 1.3  
F11 
Buell 
matrix equations, linear independence  1.4, 1.5, 1.6, 1.7  
F11 
Buell 
linear transformations  1.8, 1.9  
F11 
Buell 
linear transformations  1.8, 1.9  
F11 
Buell 
vector spaces, subspaces, column space, null space, linearly independent sets, bases  4.1, 4.2, 4.3  
W10 
Ross 
(Quiz 1) systems of linear equations and their augmented matrices, echelon forms 
1.1, 1.2  
W10 
Ross 
(Quiz 2) vector equations, linear combinations, span, solutions of matrix equations  1.2, 1.3, 1.4  
W10 
Ross 
(Quiz 3) geometric solution of vector equations, parametric solution of matrix equation Ax=b  1.5  
W10 
Ross 
(Quiz 4) linear independence, linear dependence and consequences of same; necessary & sufficient conditions on a vector b for it to be in the span of a set of (column) vectors  1.7  
W10 
Ross 
(Quiz 5) matrix multiplication, finding the inverse of A by (a) formula (b) row reduction of [AI] (c) elementary matrix products  2.1, 2.2  
W10 
Ross 
(Quiz 6) determinants and their properties  3.1, 3.2  
W10 
Ross 
(Quiz 7) characteristic polynomial, eigenvector, eigenvalue, basis for eigenspace  5.1, 5.2  
W10 
Ross 
(Quiz 8) dot product, orthogonal set, the "perp" of a column space  6.1, 6.2  
W10 
Ross 
(Quiz 9) projections, leastsquares solutions, "best fit" curves  6.5, 6.6  
F09 
Ross 
(Quiz 1) systems of linear equations and their augmented matrices, echelon forms  1.1, 1.2  
F09 
Ross 
(Quiz 2) vector equations, linear combinations, span, solutions of matrix equations, homogeneous systems, and parametric vector form of solutions  1.3, 1.4, 1.5  
F09 
Ross 
(Quiz 3) linear independence, linear dependence and consequences of same  1.7  
F09 
Ross 
(Quiz 4) matrix multiplication, finding the inverse of A by (a) formula (b) row reduction of [AI] (c) elementary matrix products  2.1, 2.2  
F09 
Ross 
(Quiz 5) subspace, row space, null space, basis  2.8, 2.9  
F09 
Ross 
(Quiz 6) determinant, eigenvector, eigenvalue, characteristic polynomial  3.1, 3.2, 5.1, 5.2  
F09 
Ross 
(Quiz 7) dot product, orthogonal basis, the "perp" of a column space  6.1, 6.2  
F09 
Ross 
(Quiz 8) least squares solutions of Ax=b  6.5  
W09 
Ross 
(Quiz 1) systems of linear equations and their augmented matrices, echelon forms, vector equations, linear combinations, span  1.1, 1.2, 1.3  
W09 
Ross 
(Quiz 2) solutions of matrix equations, homogeneous systems, and parametric vector form of solutions; linear independence  1.4, 1.5, 1.7  
W09 
Ross 
(Quiz 3) linear transformations, onto, onetoone  1.8, 1.9  
W09 
Ross 
(Quiz 4) subspaces of R^n, column and null spaces of a matrix, basis of a vector space  2.8  
W09 
Ross 
(Quiz 5) properties of determinants  3.1, 3.2  
W09 
Ross 
(Quiz 6) eigenvalues, eigenvectors, eigenspaces, characteristic polynomial  5.1, 5.2  
W09 
Ross 
(Quiz 7) dot products, orthogonal sets, row space  6.1, 6.2, 4.6  
W09 
Ross 
(Quiz 8) projections, leastsquares solutions, "best fit" lines  6.5, 6.6  
F08 
Ross 
(Quiz 1) systems of linear equations and their augmented matrices, echelon forms, vector equations, matrix equations, span  1.1, 1.2, 1.3, 1.4  
F08 
Ross 
(Quiz 2) solutions of Ax=b in terms of particular solutions and solutions of the corresponding homogeneous system, finding explicit conditions for a vector to be in the span of a set of vectors  1.4, 1.5  
F08 
Ross 
(Quiz 3) linear independence of a set of vectors, how to determine which vectors in a linearly dependent set can be written as linear combinations of the others  1.7  
F08 
Ross 
(Quiz 4) matrix operations, inverses,characterizations of invertible matrices  2.1, 2.2, 2.3  
F08 
Ross 
(Quiz 5) abstract vector spaces and subspaces  4.1  
F08 
Ross 
(Quiz 6) column and null spaces  4.2  
F08 
Ross 
(Quiz 7) determinants and their properties, eigenvectors, eigenvalues, characteristic polynomials  3.1, 3.2, 5.1, 5.2  
F08 
Ross 
(Quiz 8) diagonalization  5.3  
W08 
Ross 
(Quiz 1) systems of linear equations, row reduction, echelon forms, solutions of systems  1.1, 1.2  
W08 
Ross 
(Quiz 2) use of calculators to find RREF,analyzing solutions, linear combination and span of a set of vectors  1.3  
W08 
Ross 
(Quiz 3) homogeneous systems and particular solutions, conditions under which a vector b is in the span of the columns of a matrix A  1.5  
W08 
Ross 
(Quiz 4) linear transformations, onetoone, onto  1.7, 1.8  
W08 
Ross 
(Quiz 5) matrix multiplication, matrix inverse and usage  2.1, 2.2  
W08 
Ross 
(Quiz 6) definition of, finding, using and properties of determinants  3.1, 3.2  
W08 
Ross 
(Quiz 7) null space, basis  4.2, 4.3  
W08 
Ross 
(Quiz 8) review of some chapter 4 material: bases for row, column and null space of a matrix; eigenvalues, eigenvectors, characteristic polynomial, basis for eigenspace  5.1, 5.2  
W08 
Ross 
(Quiz 9) Leontief input/output model, diagonalization  2.6, 5.3  
F07 
Ross 
(Quiz 1) systems of linear equations and their augmented matrices, echelon forms, vector equations  1.1, 1.2, 1.3  
F07 
Ross 
(Quiz 2) matrix equations, solutions in terms of particular solutions, solutions of the homogeneous system  1.4, 1.5  
F07 
Ross 
(Quiz 3) linear independence  1.7  
F07 
Ross 
(Quiz 4) matrix multiplication, inverses and their uses  2.1  
F07 
Ross 
(Quiz 5) elementary matrices, LUfactorizations  2.2, 2.5  
F07 
Ross 
(Quiz 6) determinants, abstract vector spaces, subspaces, null and column space  3.1, 3.2, 4.1, 4.2  
F07 
Ross 
(Quiz 7) rank, bases for Col(A), for Row(A), for Null(A), eigenvectors, eigenvalues  4.6, 5.1  
F07 
Ross 
(Quiz 8) diagonalization  5.3  
F04 
Haines 
systems of linear equations  1.1 
no 

F04 
Haines 
row reduction, echelon forms  1.2 
no 

F04 
Haines 
linear combinations of vectors  1.3 
no 

F04 
Haines 
the matrix equation Ax=b  1.4 
no 

F04 
Haines 
vector equations of lines  1.5 
no 

F04 
Haines 
applications of linear systems  1.6 
no 

F04 
Haines 
linear independence  1.7 
no 

F04 
Haines 
linear transformations  1.8 
no 

F04 
Haines 
the matrix of a linear transformation  1.9 
no 

F04 
Haines 
matrix operations  2.1 
no 

F04 
Haines 
matrix multiplication, inverse of a matrix  2.2 
no 

F04 
Haines 
invertibility of matrices  2.3 
no 

F04 
Haines 
partitioned matrices  2.4 
no 

F04 
Haines 
matrix factorizations  2.5 
no 

F04 
Haines 
the Leontief InputOutput Model  2.6 
no 

F04 
Haines 
applications to computer graphics  2.7 
no 

F04 
Haines 
subspaces  2.8 
no 

F04 
Haines 
dimension and rank  2.9 
no 

F04 
Haines 
determinants  3.1 
no 

F04 
Haines 
more determinants  3.2 
no 

F04 
Haines 
vector spaces and subspaces  4.1 
no 

F04 
Haines 
null spaces, column spaces, linear transformations  4.2 
no 

F04 
Haines 
linearly independent sets, bases  4.3 
no 

F04 
Haines 
coordinate systems  4.4 
no 

F04 
Haines 
dimension of a vector space  4.5 
no 

F04 
Haines 
rank  4.6 
no 

F04 
Haines 
change of basis  4.7 
no 

F04 
Haines 
applications of Markov chains  4.9 
no 

F04 
Haines 
eigenvectors and eigenvalues  5.1 
no 

F04 
Haines 
the characteristic polynomial  5.2 
no 

F04 
Haines 
diagonalization  5.3 
no 

F04 
Haines 
eigenvectors and linear transformations  5.4 
no 

F04 
Haines 
complex eigenvalues  5.5 
no 

F04 
Haines 
inner products, length, orthogonality  6.1 
no 

F04 
Haines 
orthogonal sets  6.2 
no 

F04 
Haines 
orthogonal projections  6.3 
no 

F04 
Haines 
diagonalization of symmetric matrices  6.4 
no 