P is some invertible matrix and D is the diagonal matrix shown to the right. Show that this factorization is useful when computing high powers of A. Find fairly simple formulas for A², A³, and A* (k a positive integer), using P and the entries in D. A² = D= N O O - 00 8

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Q: Find the inverses of the matrices or show that they do not exist. -5 -3 1 -2 A B= = 1 6 = 2 -3

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Q: 4 2 0 70 all oene tril(A, -1)+ eye(4). The third row of the matrix B is: Given the matrix A: 1 2 -1…

A: Let A = 1111111111111111 tril(A,-1) = 0000100011001110eye(4) = 1000010000100001

Q: explain why the following matrix does not have an inverse A=√125 352

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Q: Prove using elements that for any square matrices A,B of the same size and constant K.…

A: For any square matrices A,B of the same size and constant K.  tr(kA+B)=ktr(A)+tr(B)

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Q: Express the inverse of the following matrix (assuming it exists) as a matrix containing expressions…

A: Solution : Given that the matrix 118-16-1k0-2-24

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Q: 1 1 1 0100 0120 00 0 Let A = Write A as C DC , where D is a diagonal matrix. Hint: You can always…

A: Given : matrix A=1110010001200000 We have to write A as CDC-1, where D is a diagonal matrix.

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A: We know that a matrix A is invertible if and only if A is non singular i.e. det(A)≠ 0

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Q: Find a formula in terms of k for the entries of Ak, where A is the diagonalizable matrix below. A =…

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Q: Express the following invertible matrix A as a product of elementary matrices: You can resize a…

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Q: Find ATA for the matrix. Show that this product is symmetric.

A: The transpose of matrix A is,

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Q: a. Which of the matrices are orthogonal (has orthonormal columns)? V3 -2 V2 V3 [1 1 -4] -2 1 Find…

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Q: Find LU factorization for the following matrix. 6 3 1 X = |-6 0 -16 8 -17]

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Q: For matrices A, B, and C, if A is invertible and AB-C, then True False B = CA-¹.

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