Orthogonally diagonalize the matrices in Exercises 13–22, giving an orthogonal matrix P and a diagonal matrix D. To save you time, the eigenvalues in Exercises 17–24 are: (17) 5, 2, –2; (18) 25, 3, – 50; (19) 7, –2; (20) 13, 7, 1; (21) 9, 5, 1; (22) 2, 0. 1 3 17. 1 3 1 3

Q: find an elementary matrix E that satisfies the given equation EC = D

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Q: In Exercises 9–10, find bases s for the null space and row space of 2. b. А —D | 4 -1 3 -1] 9. а. А…

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Q: in the factoriza

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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: QUESTION 33 Construct a 4×4 matrix to rotate 60° about the z-axis and rotate 30° about the x-axis…

A: please comment if you need any clarification. if you find my answer useful please put thumbs up.…

Q: Find a 3 x 3 matrix A such that 1 -5 A 3 A 1 -3 and -2 A 4 1 -5 A = 3. ||

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Q: 1 Given the matrix A = 2 3 3 2 3 1 6 5 4 5. 97 85 (a) Find a basis each for N(A) and C(A). What is…

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Q: (c) A(BC) = (AB)C [Associative law for matrix multiplication]

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Q: Find the matrix that represents a rotation counterclockwise around the origin by 15° followed by an…

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Q: (b) Find a matrix P which diagonalizes the matrix A = 101 010 101

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Q: 4 1

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Q: he LU decomposition of a matrix A is given as follows: L=[[1,0,0],[-2,1,0],[-3,1,1]] and…

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Q: 6. 1 -5 -4 0 3 4 -3 6 0

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Q: 3 5 4

A: Theorem 8: An Inverse Formula  "Let be an invertible matrix. Then Adjugate Matrix: Let be an…

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Q: [10 01 1 10 A = 0 1

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Q: Consider the matrix A = 1 2-2 3 6 -5 4 48-75 Find a basis for the row space of A.

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

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Q: [ 8 }] -7 -3

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Q: Solve. y" + 36y = u;(t), y(0) = y' (0) = 0 %3D S f(t) for t < 5 1 9(t) for t 5' The solution can be…

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Q: Find the coordinate matrix of x in R'" relative to the standard basis. = (2, –6, –5, 9) [x]s =

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Q: Part II [1 1 0 2 Let B = 2 2 1 1 . Then the dimension of C'(A) is 3 3 1 3 the dimension of C(A") is…

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Q: Let A be an mxn matrix. Then O A. rank(A)+ nullity(A) =n-m B. rank(A)+ nullity(A) =m+n C. rank(A)+…

A: Given that A is a m×n matrix. We have to find the value of rank(A)+nullity(A)