- 10 -20 Let A = 10 22 -10 Find an orthogonal matrix P and a diagonal matrix D such that D= p" AP. 20 -10 P - D =

Q: Please check if my steps and answer are correct. The prompt is to diagonalize the matrix  12 -21…

A: The answer is in below steps.

Q: Given matrices A, B, P such that det (A) = 2, det (P) = -3, and B = PAP-. Which one of the following…

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Q: 3 -2 -2 Verify that A s-'AS = diag(1, 2, 23). -3 -2 -6 is diagonalizable and find a matrix S such…

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Q: (b) B={(-1,3), (2, -1)} and 8' = {(0, 10), (5,0)} (c) B={(2,5), (-1, -3)} and 3' = {e1, e2} (d)…

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Q: Let A = Diagonalise this matrix. That is, find a diagonal matrix D and an invertible matrix Q such…

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Q: What are L and D (the diagonal pivot matrix) for this matrix A? What is U in A = LU and what is the…

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Q: 2 (True false) [3 4 4 3 is an or the gonal matrix ?

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Q: The i th row vector of a matrix product AB can be computed by multiplying A by the ith row vector of…

A: Given statement is  The i th row vector of a matrix product AB can be computed by multiplying A by…

Q: Suppose that Q is an orthogonal matrix, then OaQ-8 ObQ-2 d 1Q-0

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Q: Put as many 1's as possible in a 4 by 8 reduced echelon matrix R so that the free columns are(a) 2,…

A: In a reduced echelon form of a matrix, if there is a pivot element in a row then, the elements above…

Q: Write B as a linear combination of the other matrices, if possible. (If not, enter DNE in all…

A: We will find the required.

Q: If A is an m x n matrix then A' A and A have the same rank. true false

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Q: 1 31 A = 2 7 . A·B = B · A = I3×3 -2 -4 -5. ]

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Q: Number 6 (b and d only!)

A: We have to find the invertible matrix Q

Q: a) Given the matrices A = = i) A-¹. ii) BT if (3AB) = C. = (₁ 2). Find 1 (¹₁3) and C= 3 3 b) If S³R…

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Q: Find the general form of the span of the indicated matrices. (Use only x and w as variables in your…

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Q: 15. Diagonalize the matrix A = 11 expressing it similar to a diagonal matrix D. "

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Q: 16 21 Let A = |-14 -19 Find two different diagonal matrices D and the corresponding matrix S such…

A: Given matrix is A=1621-14-19 We find the eigenvectors. For eigenvalues, A-λI=0⇒1621-14-19-λ…

Q: 1 -4-2) s) Let A := -2 3 2 4 -8-5 (a) Show that A is diagonalizable and find a nonsingular P such…

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Q: If Q = I- auu' where Qis an orthogonal matrix, a > 0, and u e R"x1 real vector, and I is n x n…

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Q: Consider A = 21 2 1 3 -1 -3 4 Convert A to an upper triangular matrix U by using Gaussian…

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Q: 4 -1 5 -2 where I is the identity matrix. Let A = Compute 31 – A and (31)A,

A: To compute the following matrix

Q: Let 3 A = -1 -1 3 -1 -1 3 (a) Find a matrix P that orthogonally diagonalizes A. (b) Find B = P-¹AP…

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Q: Let 2 -1 A = 1 -1 0 2 Find an orthogonal matrix P and a diagonal matrix D such thatt D = P"AP. D =…

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Q: : 21 = |-1/v2 1/V2-1 1/V2 1/V2]1 o 01-1/v2 1/V2 31[ 1/V2 1/v2] Given the diagonalized matrix A =…

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Q: Find the change-of-coordinates matrix from B to the standard basis in R". 2 -2 3 8 -2 7 8. Pa

A: Uf7ygth

Q: Suppose A = *=([=3][=3][==] A6- -27 -15 50 28 = Find an invertible matrix P and a diagonal matrix D…

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Q: Which of the following is the matrix C that satisfies the equality (CT +312) -1 3 (a) 2 -5 (:) 5 -2…

A: First take inverse on both sides of matrix equation CT+3I2-1=2714. CT+3I2-1=2714CT+3I2-1-1=2714-1…

Q: Q2) Find x for the following matrix 3 1 x| a) -1 3 4= -30 1 ol 1 |1 2 1| b) 12 x 2=0 13 6 xl

A: We need to solve the determinant and find the value of x.  Now, if we have a 3×3 matrix…

Q: Consider the elementary matrix 1 0 -- a 2 1 Describe the action of this matrix from the left in…

A: Here →A=(1,2),→B=(0,1) The vectors A, B are linearly dependent if their determinant is zero. i.e.…

Q: [2 3 2] 10.) Is A=|0 7 6 an invertible matrix? Explain [5 5 4]

A: We have to solve the problem

Q: O Given the matrices 3-1 A =| 0 aud B=| 2 -1 31 eveluate aund simplity a) G = AB B) D = BA-3B2 c) E=…

A: We are given the matrix is A and B and we need to calculate the matrix C , D and E in simple form.

Q: If matrix A (mxn) has full rank, and I multiply it by its conjugate transpose A*. In other words,…

A: We will give a counter example that will prove this statement wrong.

Q: Which of the following statements is true for all invertible 3x3 matrices A and B? (3ABA-!)-|B =…

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Q: Enter the matrices P and D below.

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