Use the Gram-Schmidt process to find an orthogonal basis for the column space of the following matrices. -2 1 -6 -1 4 -16 -18 -2 2 -5 5 -4 2 (a) -2 (b) 2 10 21 -2 -5 5-20 -16 2

Q: Find two different 2x2 matrices A and B such that AB = BA. %3D --. .. (Use a comma to separate…

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Q: X= 3 -2 0 0 -2 1 1 0 +S 1 2 1 Find a Basis for Row B of this Matrix

A: Given:To find: A Basis for Row B of this Matrix.The row space (Row B) of a matrix is the set of all…

Q: Prove that the column vectors of the matrix B = space of the matrix B. U 2 128 0 4 2 are dependent.…

A: The given matrix .The aim is to prove that the column vectors of  are dependent and describe the…

Q: Find a QR-factorisation of 1 1 -1 1 | 1 1 1 1 0 -

A: The given question is solved below.

Q: [2a11 5a12 Let A = |2a21 5a2 -3a23 2a31 5a32 -3a33 diagonal matrix and neither B or D is equal to…

A: The given matrix isA=2a115a12-3a132a215a22-3a232a315a32-3a33.We have to factorise A into A=BD where…

Q: Find bases for row(A) and col(A) in the given matrix using AT. row (A) col(A) A = 1 -3 1 0 1 3 1 -4…

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Q: Find (a) a basis for the row space and (b) the rank of the matrix.

A: Find (a) a basis for the row space and (b) the rank of the matrix.

Q: Let A be a 3 x 5 matrix in which not all entries are zero. (a) What size must the matrix B be for AB…

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Q: Find (a) a basis for the row space and (b) the rank of the matrix.

A: To find the basis for the row space and the rank of the matrix, we will perform row operations on…

Q: Q14: Create a model using appropriate block to concatenate vertically the matrices A, B, and C…

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Q: Consider the following matrix A and its reduced row-echelon form: 5-6 103 2 12 -3-69 12-15 18 0 1 -3…

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Q: iagonalize the following matrix: 21 4 1-4 31 -1 24001₁ 111-12 C - 0

A: A matrix is diagonalizable if A.m. of each eigen value = g.m. of corresponding eigen value

Q: 2. Given the following matrices below, confirm or deny that (BT AT)-¹ = (A-¹B-¹)". 40*X B = 2 2 3 -6…

A: Given, A and B are two matrices We need to prove (BTAT)-1 = (A-1B-1)T

Q: The matrix A(4x3) = 3,-5,1 second row 1,1,1 third row -1,5,-2 fourth row 3,-7,8. Use the…

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Q: Find an orthogonal basis for the column space of the matrix to the right. -1 5 1 -7 1 - 1 1 -3 5 2 5…

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Q: Find a matrix P such that P'AP orthogonally diagonalizes A. Verify that P'AP gives the proper…

A: As this problem is related to orthogonal diagnolization of a matrix, hope you know how to find…

Q: Use the fact that matrices A and 8 are row-equivalent. 2 10 0 5 11 0 722-2 A = B = 1 2 3 10 23 7 0…

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Q: Find the characteristic polynomial of the matrix

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Q: (4) Find an orthogonal matrix P that diagonalizes A. Verify that PT AP gives the proper diagonal…

A: As per the question we are given a 4×4 square symmetric matrix A and we have to find an invertible…

Q: a. Which of the matrices are orthogonal (has orthonormal columns)? V3 -2 V2 V3 [1 1 -4] -2 1 Find…

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Q: -37 -1 0 -1 4 0 -1 -1 4 -1 0 A = 3

A: Here we use the gram Schmidt process to find the QR decomposition of matrix

Q: -1 6. 6 3 -8 3 1. Find an orthogonal basis for the column space of the matrix 1 -2 6 1 -4 -3

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Q: Find a QR factorization of the matrix [1, 2, 4] [-1, -3, -3] [0, 1, 1] [-1, -1, -1] [1, 2, 4]

A: Given matrixA=[124−1−3−3011−1−1−1124]A=QR, where Q is 5×3 matrix with orthonormal Columns and R is…

Q: Find an LU 5 -5 -10 25 -13 -13-8 factorization of the following matrices: -3 0 5 -6 9 -5 (a) 3 -1 2…

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Q: Find the LDU factorization of -3 -6 A -15 -29 33 -15 22 That is, write A = LDU where L is a lower…

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Q: 1 2 3 A = 1 3 2 2 6 8

A: See solution below

Q: Calculate LU decompositions for each of these matrices (Non-anonymous questionO) 1 3 2 A = 2 8 5 2 1…

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Q: rices in the factori

A: Given,          A=160210021