- 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: 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: [-5 -5 [-3] 1. For the matrix A 2 -3 determine (and explain why) if vector ú 3 is | 4 2 3 2 a. in…

A: GIVEN A=-5-5002-3423 to determine if vector u→=-332

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

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Q: Suppose A is an n x n matrix and B is an invertible n x n matrix. Simplify the following: a) (BAB)?…

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Q: Let (x, y, z) E R³ and the transformation T: R³ → R² be given by T(x, y, z) = (2x + 4y, x + 3y + z).

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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: Show that matrix A 5 1 0 5 cannot be diagonalized by using (λI-A)

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

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Q: 8. (3pts) Let A and B be arbitrary n x n matrices. Multiply (A – B)(A+ B).

A: As we know that (A-B)(A+B) = AA+AB-BA-BB=A2+AB-BA-B2here AB need not to be equal to the BA. Because…

Q: Let 2 -1 | -1 2 -1 -1 -1 -1 -1 –1 -1 2 -1 2 be the Eç Cartan matrix corresponding to the simple…

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Q: 11 A square matrix A is orthogonal if AA" = 1. What properties must be possessed by the columns of…

A: Given:

Q: Let B=(b₁,b₂), C=(C₁,C₂), be bases for R² b₁ = (-5,-3), b₂ =(3,2), C₁=(1,3), C₂ = (1,2) Find the…

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Q: -5 4] -5 2 1 ||

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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: 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: Diagonalize the matrix 1 0 A = -2 3 -1 -2 0 2 In other words, you need to find a diagonal matrix D…

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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: -9 4 4 1. Let A = -8 3 4 . Find an invertible matrix P and diagonal matrix D so that A = PDP-1.…

A: See the detailed solution below.

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: 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: 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: Prove or disprove: If the columns of a square n ×n matrix M are linearly independent, so are the…

A: Linearly independent and dependent vectors

Q: 10:37 01 -1 02-2 R3 → R3 -2R₂ 1 0 -2 0 1 -1 00 V₁ X2 YO x3 thus, we get x1 - 2x3 = 0 - x₂x3 = 0 let…

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Q: Find the LDU factorization of -2 -2 6 4 -15 -10 A = -6 3 -13 -14 -2 14 46 35 That is, write A = LDU…

A: Given A=−2−26425−15−10−63−13−14−2−144635. Find the LDU factorization of A.

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.