# MATH 250 Spring 2010 Schedule

DateSecPageQuestions
Mon 11 Jan1.1 Intro to Matrices, Linear Systems
Wed 13 Jan1.2 Row Operations, Gaussian Elimination
Fri 15 Jan1.3 Matrix Add, Scalar Mult, Transpose, Identity, Multiply
Mon 18 Jan1.4 Matrix Inverse
Wed 20 Jan1.5 Calculating the Inverse
HW1 1.1p. 6# 1, 4, 5, 7, 8
1.2p. 19# 2bdf, 4ac, 6bc, 7bc, 10, 14, 16, 17, 18 (no fractions), 23 (bonus: solve for arbitrary λ)
1.3p. 34# 2, 3, 4, 5, 13
Fri 22 Jan1.6-1.7 When is a System Solvable?
Diagonal, Triangular, Symmetric Matrices
Mon 25 Jan2.1 Determinants via Cofactors
Wed 27 Jan2.1-2.2 Adjoint and Inverse, Cramer's Rule, Determinant via Gaussian Elimination
HW2 1.3p. 37# 23, 29
1.4p. 49# 8, 12, 14, 16 (give an example), 21
1.5p. 58# 6ac, 7abc, 8e, 9, 22
Fri 29 Jan2.3 (skip 2.4) Properties of Determinants; Eigenvalues
Mon 1 Feb3.1-3.2 Eigenvalues; Geometry: Vectors, Dot Product
Wed 3 Feb3.3-3.4 Projections, Cross-Product, Lagrange's Identity
HW3 1.6p. 66# 3, 17, 20
1.7p. 74# 16, 22, 24 (A=LU is called the "L-U decomposition"), 28
ch1p. 77# 15 (this is called interpolation), 16, 27
2.1p. 94# 7, 9, 12, 23, 33
2.2p.101# 5, 9, 13
ch2p.119# 10
Fri 5 Feb3.4 Area of Parallelogram, Volume of a Parallelepiped
Mon 8 Feb3.5 Lines/Planes: vector forms, point-normal form
Wed 10 Feb4.1-4.2 Distance from point to plane; Euclidean n-space
HW4 2.2p.103# 21 (for n x n; each add/mult counts as one op)
2.3p.110# 5, 13, 23 (prove or show a counterexample!)
3.1p.130# 9, 19, 20
3.2p.134# 4, 12
3.3p.142# 3 (say why), 4, 11, 28
3.4p.154# 18, 19
Fri 12 Feb4.2 Properties of Inner Product; Linear Transforms in R3
Mon 15 Feb4.3 Transforms: Scaling, Rotation, One-to-one
Wed 17 Feb-.- Midterm 1 (ch1-§3.4)
Fri 19 Feb4.4 Visualizing Linear Transforms, Determinant, Eigenvalue
Mon 22 Feb (Independent Study Week; no class)
Wed 24 Feb (Independent Study Week; no class)
Fri 26 Feb (Independent Study Week; no class)
Mon 1 Mar4.4 Space of Polynomials, Affine Transformations
Wed 3 Mar4.4 Polynomial Interpolation: Vandermonde vs. Newton
HW5 3.4p.153# 4, 10, 30
3.5p.163# 11, 24, 33, 45
4.1p.178# 6, 10, 16, 24, 26, 37
4.2p.194# 7, 8, 17, 21, 32
Fri 5 Mar5.1 Axioms of Vector Spaces
Mon 8 Mar5.2 Subspaces
Wed 10 Mar5.3 Linearly Independent Sets of Vectors
HW6 4.3p.207# 6, 14, 16, 18 (see answers for 19), 22, 28
4.4p.217# 2, 3, 5, 8, 13, 14, 19
Fri 12 Mar5.4 Vector Bases and Dimension of Space
Mon 15 Mar5.5 Column-Space, Row-Space, and Null-Space
Wed 17 Mar5.6 Rank + Nullity = # Columns
HW7 5.1p.226# 6, 8, 14, 15, 26, 27, 31
5.2p.238# 2, 3, 6, 13, 21, 25
5.3p.248# 2, 8, 14, 16, 21
Fri 19 Mar6.1 Inner Product Spaces
Mon 22 Mar6.2 Norm, Distance, Angle, Orthogonality
Wed 24 Mar6.3 Orthonormal Bases, Gram-Schmidt Process
HW8 5.4p.263# 2, 4, 5, 10, 18, 24, 32
5.5p.276# 6(acd), 8(acd), 12, 15
5.6p.288# 2(acd), 12
ch5p.290# 2, 4, 8, 12 (hint: think about a basis for all 2x2 matrices)
Fri 26 Mar6.4 QR Decomposition, Least Squares Approximation
Mon 29 Mar3.5-5.6 Review §3.5-5.6
Wed 31 Mar3.5-5.6 Midterm 2
Fri 2 Apr (Good Friday; no class)
Mon 5 Apr (Easter Monday; no class)
Wed 7 Apr6.4-6.6 Orthogonal Matrices, Least Squares Approximation
HW9 6.1p.304# 6, 10, 18, 28(ab)
6.2p.315# 6, 18(ac), 31, 34
6.3p.329# 16, 24(acd)
Fri 9 Apr7.1-7.2 Eigenvectors and Diagonalization
Mon 12 Apr7.2-7.3 Orthogonal Diagonalization
Wed 14 Apr7.3 Diagonalization
HW10 6.1p.306# 24
6.2p.315# 16, 38
6.3p.329# 18, 29, 30