MAT223H5 Study Guide - Midterm Guide: Identity Matrix, Cancellation Property, Scalar Multiplication
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MAT223H5 Full Course Notes
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Topics and practice problems for test 2: section 1. 9: the matrix of linear transformation: (1) if t : rn 7 rm is a linear transformation, then t (x) = ax where. Exercises: 20, 22, 25-28: section 2. 1: matrix operations: (1) de(cid:12)nitions of addition, scalar multiplication and product of matrices. (2) properties of matrix multiplication (associativity, distributivity, identity ma- trix). Notice that matrix multiplication is not commutative that is ab = ba in general. Cancellation law does not hold for matrices. (3) transpose of a matrix. Relation between elementary matrices and row opera- tions. (5) algorithm for (cid:12)nding a (cid:0)1. Exercises: 8,9, 10, 13, 18, 32: section 2. 3: characterization of invertible matrices: (1) the invertible matrix theorem (without proof). (2) de(cid:12)nition of invertible linear transformation. The standard matrix of an invertible linear transformation.
