(3) A square matrix A is said to be nilpotent, if some power of it is equal to the zero matrix, that is Ak = 0, where k is the smallest postive integer that satisfies the equation. Let A = 0 2 3 004 000 (a) Find the value of k for the nilpotent matrix A. (i) 0 (ii) 2 (iii) 3 (iv) 4 (v) None of the above (b) Compute e. Select the correct answer. (i) (ii) (iii) (iv) A = A = 0 0 4 000 00 0 27 004 -6 A = 0 0 0 1 2 7 0 --(14) A = 0 001 0 2 11 0 4 -(9) 0 0 (v) None of the above

Q: For each of the following, factor the matrix A into a product QDQ" where Q is orthogonal and D is…

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Q: 2. (i) Find a matrix X such that (ii) Find a matrix Y such that 1 - 32] x = [3] X -2 21 53 Y = 0 2²…

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Q: Find the RREF of the matrix -4 1 -3 من که من 2 3 -1 4 -2 3 2

A: to find the row reduced echelon form of -4       31      - 1-3       42       - 23        2

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A: We find inverse of A then fin matrix X.

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Q: 5 -3 Find the matrix A if (I+ 2AT) ¯ = | 1: -2

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Q: 1. Consider the following matrices: (b) [2 0 1 -2 ------# C= 1 3 D= 3 2 0 -1 -1 (c) A = 53 Evaluate,…

A: Consider the following matrices.To evaluate the following:

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A: 12AXB+A=2A-B

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Q: A. For any matrix A, give a simpler name for the matrix (At)t. B. Is it true or false that (2A)t =…

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Q: Find (IM)1 and X. 0.7 0.2 13 M = |; D = 0.1 0.4 28 Calculate (IM)- 1. Select the correct choice and,…

A: Step 1:Identity matrix is :I=[10​01​]Given matrix is :M=[0.70.1​0.20.4​] Step 2:Then,…

Q: you explain this part? I'm finding myself confused as to how you got the 1/3 [2 -1, -1 2] matrix

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Q: = 5.8. Let f₁(x) = x³ x² +1, f₂(x) = x³ + x² + x and f3 (x) = x³ + 2x²+3x+1 be three polynomials in…

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Q: For each of the following cases, find the matrix R that implements the indi- cated elementary row…

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Q: (c) Consider the quadratic form f(x1, x2, x3) = 3(a₁x₁ + a2x2 + a3x3)² = 4(b₁x₁ + b₂x2 + b3x3)². (i)…

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Q: 6) Let I denote the 2 x 2 identity matrix. (i) Given the equation: (1+24¹) 1 12 26 T (ii) Given the…

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Q: x-2 1. A= 3x-6 4x-11 Given that the matrix A is singular, find the possible values of x.

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Q: - Which of the following operations can we perform for a matrix A of any dimension? (i) A + A (ii)…

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