Let A and B be square matrices of order 4 such that |A| = -4 and |B| = -4. Find the following. (a) |AB| (b) |A³| (c) [3B| (d) |(AB)™| (e) |A-1|

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A: The symmetric matrix for quadratic form ax12+bx22+cx32+dx1x2+ex2x3+fx1x3 can be written as…

Q: 3. Let 1 B -1 Consider T : R²,2 → R²2 defined by T(A) = AB – BA. Let - 이 [0 [o o] [o o] [1 0] Bị and…

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Q: If X is an unknown matrix And A and B are known : [A]×[x]=[B]_ 5x5 5×1 [x] = ?

A: Given matrix A is of order 5×5 and matrix B of order 5×1 and A5×5×x=B5×1 We have to find the matrix…

Q: Diagonalize the matrices below, if possible: (a) [1 0 3 2 1 2 0 0 2] (b) [3 1 1 −4 −2 −5 2 2 5]

A: To Diagonalize the given matrices (a)[1   0  32  1   20  0  2]  (b)[3  1   1− 4 −2 −5 2  2  5]

Q: 1 2 -4 -8 (b) -2 -4, 8 16 This set is

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Q: Use the given definition to find f(A): If f(x) = a, + a,x + a,x2 + ... + a,x" is a polynomial…

A: We have to find f(A).

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A: Answer

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A: This is a problem related to matrix. We will find out square of the matrix and then calculate f(A)…

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A: To find:  and .

Q: ) Let A, B be matrices with real coefficients. (a) Find A and B such that AB is defined and BA is…

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Q: Determine whether the matrix is symmetric.

A: Now the transpose of this matrix is,

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Q: adioint of the matrix.

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Q: (b) Find a real symmetric matrix C of the quadratic form: Q(x1, x2, x3) = x+ 4x3+ 6x3+ 2x1x2…

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