We will use the book `Linear Algebra with Applications', 6th Edition, by Steven Leon. The following syllabus is only a rough outline (we may occasionally skip or add some material, or we may move slower or faster depending on how the class goes)
Lec. 1: Sec 1.1: Systems of linear equations.
Lec. 2: Sec 1.2: Row echelon form.
Lec. 3-4: Sec 1.3: Matrix algebra; Consistency Theorem.
Lec. 5: Sec 1.4: Elementary matrices; triangular (LU) factorization.
Lec. 6: Sec 1.5: Partitioned matrices. (might get skipped)
Lec. 7: Sec 2.1: The determinant.
Lec. 8: Sec 2.2: Properties of determinants.
Lec. 9: Sec 3.1: Euclidean vector spaces, pp. 125-129.
Lec. 10-11: Sec 3.2: Subspaces.
Lec. 12: Sec 3.3: Linear independence.
Lec. 13: Sec 3.4: Basis and dimension.
Lec. 14: Sec 3.5: Change of basis, pp. 163-169.
Lec. 15: Sec 3.6: Row space and column space.
Lec. 16: Sec 5.1: Scalar products, Cauchy-Schwarz, projections.
Lec. 17: Sec 5.2: Orthogonal subspaces.
Lec. 18: Sec 5.3: Least squares problems.
Lec. 19: Sec 5.5: Orthonormal sets; orthogonal matrices, pp.270-274.
Lec. 20: Sec 5.6: Gram-Schmidt; QR factorization, pp. 290-296.
Lec. 21-22: Sec 6.1: Eigenvalues and eigenvectors; similar matrices.
Lec. 23: Sec 6.3: Diagonalization by similarity.
Lec. 24-25: Sec 6.4: Hermitian matrices; Schur's Theorem; Spectral Theorem; normal matrices.
Lec. 26: Sec 6.5: Singular Value Decomposition
Lec. 27: Sec 6.6: Quadratic forms.
Lec. 28: Sec 6.7: Positive definite matrices.
Lec. 29: Review??