Practice problems for M515

    From Laub:

    Chap 1: 1, 2(first question only), 4, 5a, 5c, 6a, 6b (recall that sin(2θ)=2sin(θ)cos(θ) and that sin²(θ)+cos²(θ)=1)

    Chap 2: 1, 2, 4, 5

    Chap 3: 3, 7, 9, 10

    Chap 5: 4, 5, 6

    Chap 6: 3, 4

    Chap 7: 2, 5, 6, 8, 9

    From Strang, 3rd edition:

    Matrix multiplication/2.1/10-13    Gaussian elimination/2.2/1, 2, 11, 12    Matix arithmetic/2.4/3, 4, 5

    Matrix inverse/2.5/22, 23    Rank/3.3/2    Determinants/5.1/1, 2, 13

    Vector spaces/3.1/ 9, 10, 11, 16, 17, 18    Independence,Basis,Dimension/3.5/ 1, 5, 11abd, 16, 17abc, 19, 27, 29, 41

    The four subspaces/3.6/ 2, 3

    SVD/6.7/ 1-5

    Projections/4.2/ 1, 3, 11-13

    Least Squares/4.3/ 22/ 27

    Orthogonality, Gram-Schmidt/4.4/ 1, 2, 11, 15, 21, 22

    Norms and Condition Number/9.2/ 2, 4, 11, 12

    Eigenvalues and Eigenvectors/6.1/ 3-6