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On the other hand x 26 differentiation elementwise

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Unformatted text preview: combining it with the others results in 20. Suppose that A is nonsingular, and that there exist matrices B and C, such that AB I and AC I Based on the properties of matrices, it follows that AB C AY 0 Write the difference of the two matrices, Y , in terms of its columns as Y yy y. The -th column of the product matrix, AY , can be expressed as A yj . Now since all columns of the product matrix consist only of zeros, we end up with homogeneous systems of linear equations A yj 0 , Since A is nonsingular, each system must have a trivial solution. That is, yj for . Hence Y 0 and B C 21 0 , . ________________________________________________________________________ page 349 —————————————————————————— CHAPTER 7. —— A B . Based on the standard definition of matrix multiplication, AB . A . Note that A C. Therefore A . The result can also be written as 23. First note that ________________________________________________________________________ page 350 ————————————————————...
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