(ii) T F S is a diagonalizing matrix for A if and only if (S-¹)T is a diagonalizing matrix for AT.

Q: Find an LU factorization for the matrix A = -2 3 4 1 -3 0 2 3-2, Verify that LU = A.

A:

Q: In linear algebra, if a vector is in the range of a matrix A, then it is also in the null space of…

A: The given statement is False.

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).

A:

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

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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: e/ By three ways Show that B= %3D isorthogunal matrix

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Q: R={(2,1),(3,1),(3,2)} as a zero to one matrix

A: Given R = R=2,1,3,13,2  we have to write it as a zero-one matrix  A= 0001001103×3

Q: 1 1 -4 -2

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Q: Let A, be Hermitian matrix witho (A) = 1,-1 and B, is a Hermitian matrix with o (B) = 0,-2, then one…

A: We have to solve given problem:

Q: If A=XDX−1 where  X is a diagonalizing matrix of A, then 7X is also a diagonalizing matrix of A.…

A: Given: Where, X is a diagonal matrix of A, then 7X is also diagonalizing matrix of A. To determine:…

Q: 1 3 3 - 4 1 A(x)=x² – A -2x+3 5 2

A:

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: 6. Find the distance between the matrices A and B, p(A, B), using the ||- ||2 for the matrix -[:] -1…

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Q: 1. (Your instructor forgot to do this example in class). Let W = = Span (a) Find a matrix A so that…

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Q: -() --()-() 3 6 3 3 1 2 1 2 1 1 2 1 3 1 2 3 2 2 A = 3 1 2 В C = 4 4 3 4 4 3

A: Claim: We have to find E such that EA=Bi.e. E=BA-1 And F such that, FA=C i.e. F=CA-1 A=121312443then…

Q: Exercise 51. Is there a square matrix X with real entries such that det(X¹X) = -3?

A: detXTX=-3 X is a square matrix with real entries.

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: Let B = {(1, 3), (-2,-2)) and B' = {(-12, 0), (-4, 4)) be bases for R2, and let A = 02 be the matrix…

A: As per guidelines of bartleby we solve only first three parts.

Q: Use matrix multiplication to find the contraction of (a,b) with factor k =1 / alpha, where alpha is…

A:

Q: TRUE or FALSE: Every invertible n xn matrix is similar to the identity matrix In.

A: To state true or false given statement.

Q: Let A be a square, invertible matrix and let A' be its transpose. Which of the following statements…

A: Solution

Q: Find an explicit description of NulA by listing vectors that span the null space, where [1 5 -4 -3…

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Q: Determine all the n × n− matrix A with the range such that A2 = A.

A: Clearly the zero matrix and identity matrix are the trivial examples of our problems. However there…

Q: 3. Let f R→ R³ and g: R³ → R be defined by f(t)= (t2, sin(t), et) and g(x, y, z) = xy + z. Using…

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Q: How would I write the following 2 functions in matrix notation? Q(h) = (h, 2h, 3h) F(x, y, z) =…

A: We have to write the function as matrix notation. The given function is Q(h) = (h, 2h, 3h) Clearly,…

Q: 5 3 [B] -5 -6 i.e. write A = LU where L is a lower triangular matrix with 1's on the diagonal, and U…

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Q: If X and Y are two full column-rank matrices of rank p, find all matrices A for which R(A) = R(X)…

A: Here given that are two column rank matrices of rank  so that where .Obviously  .From above…

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: b) Evaluate det[(2A)-1 (3A")], where A is any invertible (2 x 2) matrix.

A:

Q: 3. Choose the matrix that is equal to the matrix below. 0.82 2 12 4 5 9 19 082 2 0.6 [B] 12 4 10 3…

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Q: Diagonalize the matrix -5 -2 A = 3 [ by writing it as A = PDP-1

A: