Stitz-Zeager_College_Algebra_e-book

1 solve 2x1 3x2 4 for x1 and x2 5x1 x2 2 2x 3y

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Unformatted text preview: columns. Note that to in order to verify that the identity matrix acts as a multiplicative identity, some care must be taken depending on the order of the multiplication. For example, take the matrix 2 × 3 matrix A from earlier 2 −10 A= 0 −1 3 5 In order for the product Ik A to be defined, k = 2; similarly, for AIk to be defined, k = 3. We leave it to the reader to show I2 A = A and AI3 = A. In other words, 10 01 2 −10 0 −1 3 5 = 2 −10 0 −1 3 5 and 100 0 1 0 = 001 2 −10 0 −1 3 5 2 −10 0 −1 3 5 While the proofs of the properties in Theorem 8.5 are computational in nature, the notation becomes quite involved very quickly, so they are left to a course in Linear Algebra. The following example provides some practice with matrix multiplication and its properties. As usual, some valuable lessons are to be learned. Example 8.3.2. 1. Find AB for A = −3 2 and B = 1 5 −4 3 −23 −1 17 46 2 −34 2. Find C 2 − 5C + 10I2 for C = 1 −2 3 4 3. Suppose M is a 4 × 4 matrix. Use Theorem 8.5 to expand (M − 2I4 ) (M + 3I4 ). Solution. 1. We have AB = −23 −1 17 46 2 −34 −3 2 1 5 = −4 3 00 00 2. Jus...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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