II. Is the matrix C=0 i 0 € M3 (C) diagonalizable? Justify your answer. 02

Q: Show that the matrix A is positive definite A = 2 1 12

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Q: If A and B are similar, then there exists a matrix P such that B = PAP. Use this fact to fi -2 2 -3…

A: Here we have to find B5 ,   We have to find if A and B are similar or not, if A and B are similar…

Q: For the matrix A = 2 3 20 06 7 3 what is the value of |A|?

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Q: Q1: If you have the following matrix 0.2 X1 - 0.7 X2+ 0.4 X3 0.6 X1-0.5 X2 + 0.8 X3 = -0.14 -33 0.4…

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Q: Consider the matrix c-[:| 6 3 C = -5 4] What is the value of C? |C| =-9

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Q: Q3. Find the rank of the following matrix A by reducing it into echelon form: 1 2 1 3 A = 5 3 5 7 7…

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Q: Determine the matrix if it is a linear combination of O A.c = 5; d = 8 O B. c = -5;d =8 O C.c = 8; d…

A: 12cd = a1-1-1-1 +b3159 + m41611 + n-1234 Therefore, we get a+3b+4m-n = 1…

Q: Q1: Given that A = [3 -3 -5] and B = 5,what is the matrix A- BT?

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Q: [2х 81 2) For what values of (x) does the matrix : 1 a)singular b) non-singular

A: Given matrix is  A=2x81x Now,  A=2x81x=2x2-8=2x2-4 So, A is singular when A=0 which occurs when x2-4…

Q: 9. When can a square matrix be diagonalized? When can a square matrix be diagonalized orthogonally?

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Q: Given the matrix m M A. What value of m makes a factorization M = QAQ" possible? Justify your…

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Q: [1 0 2] 1 2 is diagonalizable. Justify your answer. 0 0 0 9. Determine if the matrix A = 1

A: If minimal polynomial having a repeated roots then that matrix is not diagonalzible.

Q: Ex check the Convergency of the Pollowing sequences. (5 メフ6 2n + 1

A: converges of the sequence

Q: 8 9 11 12

A: matrix A is in dimensions 2*3 Matrix B is in dimensions 3*2 So multiplication of A and B= [AB] [AB]…

Q: H5. Consider the matrix 0 c-[98] C= -1 0 First, show that C² = -I and use this relationship to…

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Q: 1 For the matrix A = 2 3 -2 0 7 4 6 3, what is the value of |A|?

A:

Q: 2 4 -1 -2] whatever size you like. 3-16. If A = " find a non-zero matrix B such AB = 0, where 0 is a…

A: The given matrix is; A=[2 4     -1 -2]AB=0Find the matrix B.

Q: Q3. Diagonalise the matrix [A]. 4 33 [A] = 3 6 1 3 1 6

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Q: Use as many columns of A as possible to construct a matrix B with the property that the equation Bx…

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Q: Let A E Mn(C) denote the n x n matrix with all entries equal to 1. Show that A is positive…

A: Let A belongs to  Mn (C) denote the n x n matrix with all entries equal to 1. Show that A is…

Q: Produce a matrix P that diagonalizes the matrix below. Determine P1AP. [5 0 1 0 Lo o -21 3

A: Consider the given matrix.

Q: Compute the product using the methods below. If a product is undefined, explain why. a. The…

A: Given Axfind the product using the linear combination of two columns of the matrix A==