Section 1.1: Systems of linear equations. Matrices, Linear equations and their solutions, systems of linear equations and their solutions, augmented matrix, size, scalars, column and row matrices and notation.
Pages 8-10: 1,3,5,7,9,11,17
Section 1.3: Matrices and matrix operations. Entries of a matrix, square matrices, equality of matrices, main diagonal, matrix arithmetic (addition, subtraction, scalar multiple, multiplication), partitioned matrices, matrix multiplication by columns and by rows, linear combinations, transpose, trace and matrix form of a linear system.
Pages 36-38: 1-6, 12-14, 18, 21, 29, 32
Section 1.5: Elementary matrices and a method for finding inverse. Elementary matrices and their inverses, row operations represented by matrix multiplication, inverse row operations and Theorem 1.5.3 of equivalent statements. Row equivalences, method of finding Inverse of A.
Pages 58-60: 1-20, 23, 24, 27
Lecture notes - pink button - My lecture notes from class.
Suggested homework exercises - As listed.
Section 2.1: Determinants by cofactor expansion. Minor of entry a_ij and cofactor of entry a_ij. Determinants by cofactor expansion along any row or column. Matrix of cofactors, adjoint of a matrix, using adjoint to find the inverse, determinant of triangular matrices and Cramer's rule.
Pages 111-112: 1-32, 35, 36.
Pages 127-128 (Cramer's Rule): 24-29, 31, 32.
Pages 127-128 (Adjoint Method): 19-23.
Section 2.2: Evaluating determinant by row reduction. Some properties of determinant (transpose, proportional rows or columns). Effect of row operations on determinants and determinants of elementary matrices. Evaluating determinant by row reduction, using column operations and combining cofactor expansion with row operations to find determinant.
Pages 117-118: 1-28
Section 2.3 : Properties of the determinant function. Properties of the determinant of a scalar multiple of a matrix, of the product of matrices and of the inverse of a matrix. Theorem of invertiblity in relation to determinants.
Pages 127-128: 1-18, 32, 33, 34, 35, 36, 37
Section 1.6: Further results on systems of equations and invertibility. Theorem on solutions of linear systems, solving linear systems by matrix inversion and how to solve multiple systems with the same coefficient matrix. Theorems of invertibility for square matrices. Finding b matrices such that Ax=b is consistent.
Pages 66-67: 1-6, 9, 12, 13, 14, 18
Section 1.2: Gaussian and Gauss-Jordan elimination. Elementary row operations, free variables (and parameters), constraint variables, REF, RREF, Gaussian elimination algorithm, back substitution, Gauss Jordan elimination algorithm and homogeneous systems.
Pages 22-25: 1-14, 15-19, 23, 25-28, 31, 36
Section 1.4: Rules of matrix arithmetic and definition of inverse. Properties of matrix arithmetic, properties of zero matrix and identity matrix and definition of matrix inverse. Inverse of any 2 X 2 Matrix, Theorems on invertibility, powers of a Matrix and laws of exponents for matrices. Polynomial expression of a matrix and Theorems of transpose and transpose invertibility.
Pages 49-52: 1-22, 39
Section 1.7: Triangular (Upper, Lower, diagonal) & Symmetric matrices. Properties of symmetric matrices. Invertibility of symmetric matrices. The product of a matrix with its transpose is symmetric.
Pages 72-75: 1-14, 17, 19, 20, 31, 32, 34
3.5
Eigenvalues
&
Eigenvectors
Midterm Exam: Chapter 1 and 2.
Liliana Menjivar
Instructor