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Linear Algebra with Applications

Time Section Suggested Problems
1 1.1 Matrices and systems of linear equations 5,6, 7, 10, 11, 12, 13
1 1.2 Gauss- Jordan elimination 2,3,6, 7, 10, 13
1 2.1 Operations on matrices 5, 10, 13, 14, 15, 16, 19,20
0.5 2.2 Properties of matrix operations 1,5, 7, 8, 9, 10, 19,20,23,24,28
0.5 2.3 Symmetric matrices 1,2,5, 10, 11, 12, 13
1 2.4 Inverse of a matrix 2,4, 7, 9, 11, 14, 15, 18, 19,22,24,25,26
1 3.1 Introduction to determinants 4,7,8,10,11,13,14,15
1 3.2 Properties of determinant 2,3,5, 7, 9, 11, 15, 16, 19
0.5 3.3 Numerical evaluation of determinants 4,6, 11, 12, 14
1 3.4 Determinants, matrix inverses, and
systems of linear equations
4,7,10,14,15,17,19,20,21,22,26
0.5 4.1 The vector space Rn 3,4, 7, 10, 12
1 4.2 Dot product , norm, angle, and distance 2,4,6,10,13,14,16,19,20,22,30,32
1 4.4 Subspaces of Rn 2,4,5,8,10,11,12
1 4.5 Linear combinations of vectors 3,5, 7,8,9, 11, 18
1 4.6 Linear dependence and independence 2,4,5,7,8,9
1 4.7 Basis and dimension 3,4,5,6, 7, 8, 11, 13, 14, 15, 16
1 4.8 Rank of a matrix 2,5,6, 7,8,9, 11, 12, 14, 15
1.5 4.9 Orthonormal vectors and projections in Rn 2,3,4,6, 7, 8, 9, 10, 14, 16, 17, 18
0.5 6.4 Solutions of homogeneous and and non-homogeneous systems 1,3,5,6, 10, 11 + supplementary problems
from handout

TOTAL: 17 periods of lectures + 3 periods for tests and review; 1 period=75-minute lecture.

* Omit projection onto a subspace.

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