Let A be a diagonalizable n x n matrix and let P be an invertible n x n matrix such that B= pAP is the diagonal form of A. Prove that ak = Petp-, where k is a positive integer. Use the result above to find the indicated power of A. [-6 0 4] A = -5 -1 4 -6 0 4

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A: The given equation is,

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Q: b. Prove: If A is an mxn matrix and A(BA) is defined, then B is an n xm matrix.

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Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.