5. Finding a generating set for the column space and null space of the matrix 1 1 -1 21 A = -1 -2 1 2 3 1 4

Q: Г1 2 3 4 5 A = 5 0 2 4 6 8 5 5 5 5

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

A: The given question is solved below.

Q: 2. Find bases for i) the row space, ii) the column space, and iii) the null space of the matrix 3 -3…

A: The given problem is to find the bases of row space , column space , null space of the given matrix.

Q: Original Matrix -2 5 1 New Row-Equivalent Matrix 18 [": 0-34 4-1 -7 -7 O Add 6 times Row 2 to Row 1.…

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Q: Assume that the matrix A is row equivalent to the matrix B where A = 1 1 -3 7 9 -9 without…

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Q: a) Using elementary row operations 1 (ERO), convert matrix A = 3 2 to matrix 3 B = 2 4 1 Is it…

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Q: b) The following proposed proof contains two mistakes. Explain the mistakes. Result Let A and B be…

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Q: find A*B and B*A for the matrices A= 10 1 2 1 1 3 2 -1 B= 0 0 3 1 2 4 -1 -1 0

A: We have to find AB and BA for the matrices                                             A=10121132-1…

Q: 1 2 10. Let A = ; ). 3 2 1 a. Find the column space for A and state its dimension. b. Find the null…

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Q: erform the row operation ( − 1)R₁ + R₂→R₂ on the matrix below. 1 -4 6 2 -7 -8 (-1)R₁ + R₂ R₂ 1 -4 6…

A: To apply the given operation to the given matrices.

Q: Let A be a $3\times 4$ matrix with null space being the span of The reduced row echelon form of A is…

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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: Diagonalize the following matrix: 1 13 5 7 -5 -7 -1 -1 7 90 06 0 00-12 060 − 1 1 − 1| -1 0 1 1 10 1…

A: Given matrix 11357-5-7-1-17

Q: To determine whether a set of n vectors from R" is independent, we can form a matrix A whose columns…

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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: Find a matrix X such that AX=B 0 6 A = [²2 -B = [1 2 ] 91 L7 8. 4

A: Given that we have to find a matrix  .Obviously order of the matrix  is .Let Now so  ,

Q: Find a basis for the column space of the matrix A || 102 2 14 326

A: Linear transformation

Q: ven a matrix A in its RREF form 0 A=1 0 0000 ܘܘܘܘܐ 1 €0-000 ooow 00100 0 0 Tota Compute the bases…

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Q: Find bases for the row space and column space of A. -2 -3 -5 A 1 1 1 2 4 3 2 9 7 6 5213 2 -3

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Q: Find orthogonal bases for the null space and for the range of the matrix  [1, 0, 0, 3; 1, 1, 0, 4;…

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Q: of the null space and the dimension of the column space of the -6 8 12 3 -47 2 12 4 -6 6 -8 (a)…

A: We know that  rank(M) = dim( Col(M))

Q: Find a basis for the row space of the matrix 2 4 -5 2 3 A = 6 -8 3 -5 -3 -6 -7 -3 -10)

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Q: 4 = = - (13 + 2) 0 3 13 -13 13 + 2 0 9. 1 B = 1 13 +3 4 -(13+ 4) [13 13+1 1 0 Calculate the…

A: Matrix multiplication is defined as row by column multiplication where the elements of the ith row…

Q: Put the following matrices into reduced row echelon form and find the null space. Do the work on a…

A: According to bartleby guidelines we are supposed to do only three sub parts.  If you want more to be…

Q: Diagonalize the following matrix: 21 0 4 - 1 -4 3 1 - 1 400 0 1 0 00-2 not diagonalization 40 0 02 0…

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Q: Let A and B be the matrices as shown. '1 2 1 1 2 1 ^ - ( ²³ ) ·- - 6 ÷ ³) A = 0 5 1 B = 2 -1 4 2 −1…

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Q: Find the sum of matrix AxB and matrix C. ((AxB)+C)

A: In this question we have to perform the following operation on the given matrices.

Q: Find a basis for the column space of -2 4 4 A = 3 3 4 -2 -16 -8

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Q: Diagonalize the following matrix: 1 13 5 7 -5 -7 -1 -1 7 not diagonalizable 60 0 -1 1 1 0-9 0 = 0 1…

A: Solution:-

Q: Use row operations to change the matrix to reduced form. 1 1 1 18 345 28 1 1 1 18 345 28 ][

A: The given matrix: 1113451828.We need to perform row operations to  change the matrix to reduced…