Stitz-Zeager_College_Algebra_e-book

Our last application of determinants is to develop an

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Unformatted text preview: t as x2 means x times itself, C 2 denotes the matrix C times itself. We get 8.3 Matrix Arithmetic 485 2 − 5C + 10I2 = 1 −2 3 4 = 1 −2 3 4 = −5 −10 15 10 = C2 00 00 −5 1 −2 3 4 1 −2 3 4 + + + 10 10 01 −5 10 −15 −20 + 10 0 0 10 5 10 −15 −10 3. We expand (M − 2I4 ) (M + 3I4 ) with the same pedantic zeal we showed in Example 8.3.1. The reader is encouraged to determine which property of matrix arithmetic is used as we proceed from one step to the next. (M − 2I4 ) (M + 3I4 ) = = = = = (M − 2I4 ) M + (M − 2I4 ) (3I4 ) M M − (2I4 ) M + M (3I4 ) − (2I4 ) (3I4 ) M 2 − 2 (I4 M ) + 3 (M I4 ) − 2 (I4 (3I4 )) M 2 − 2M + 3M − 2 (3 (I4 I4 )) M 2 + M − 6I4 Example 8.3.2 illustrates some interesting features of matrix multiplication. First note that in part 1, neither A nor B is the zero matrix, yet the product AB is the zero matrix. Hence, the the zero product property enjoyed by real numbers and scalar multiplication does not hold for matrix multiplication. Parts 2 and 3 introduce us to polyn...
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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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