SyDe114  Linear Algebra Assignments and Solutions 
Stephen
Birkett

Research
Teaching
Linear Algebra
Topics and Lectures Assignments MiniTests Numerical Methods Computational Mathematics Musical Instruments Music

Suggest assigned problems and links to solutions are listed below for each unit. I may add to this list, or adjust it to fine tune, as we proceed with the course. So check back here regularly. References are to Schaum's Outline, Linear Algebra, 3rd Edition, 2001. Try doing the problems before looking at the solutions!  
UNIT 1  VECTOR SPACES  
vector space
axioms
 4.7173  
Euclidean spaces  1.41ab, 1.43ab, 1.46, 1.47  
complex numbers  1.6669, 1.70abc  
subspaces  4.75, 4.77, 4.78, 4.8082  
linear combinations  4.8385  
linear independence  4.8991, 4.93  
basis & dimension  4.97, 4.98, 4.101103  
matrix rank, rowspace  4.1044.113  
coordinates  4.128133  
miscellaneous  4.134136  
UNIT 2  MATRIX ALGEBRA  
matrix multiplication  2.38, 2.39,2.50  
inverses  2.53, 2.54, 3.67[use row reduction method]  
echelon, rowcanonical  3.62  
elementary matrices  3.65, 3.66  
determinants  8.38ace, 8.40ab, 8.41, 8.43a  
cofactors/adjoint  8.44  
UNIT 3  LINEAR MAPS  
linear maps  5.49, 5.50bd, 5.515.53, 5.56b, 5.57b, 5.58b, 5.70, 5.71  
kernel & image  5.61, 5.62bc, 5.635.667  
invertible & nonsingular maps  5.56a, 5.57a, 5.58a, 5.76, 5.79, 5.80  
matrix representations  6.376.42  
change of basis  6.47d, 6.486.50  
matrix rep & change of basis  6.52, 6.53, 6.54a, 6.55, 6.56ac, 6.59  
UNIT 4  EIGENVALUES, EIGENVECTORS & DIAGONALIZATION  
eigenvalues & eigenvectors  9.45ab, 9.46, 9.48, 9.49, 9.51, 9.53, 9.54  
UNIT 5  INNER PRODUCT SPACES & ORTHOGONALITY  
inner products  7.57, 7.59, 7.60b, 7.62  
applications in Rn  1.41, 1.43, 1.44c, 1.45  
applications in Cn  7.917.93  
lines & planes  1.51, 1.52, 1.55 [and distance Q to H], 1.62, 1.64  
orthogonality  7.64, 7.667.69  
orthogonal projection & bases  7.74bc, 7.757.77, 7.94  
orthogonal matrices  7.81, 9.56bc, 9.57a  
UNIT 6  LINEAR SYSTEMS  
homogeneous systems  3.573.60 ,4.99b,4.100b  
equations of a line in Rn  1.53, 1.56  
nonhomogeneous systems  3.52ab,3.533.56  