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: 20. Let 1 0 −1 2 1 3 -1 A = -2 1 4 -1 3 3 -1 -5 1 -6 (a) Find a 5 x 5 matrix M with rank 2 such that…

A: Let .(a) Find a  matrix  with rank 2 such that , where  is the  zero matrix.

Q: 1. 1 3 2 3 1 6 5 4 5 39785 Given the matrix A= 2 (a) Find a basis each for N(A) and C(A). What is…

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Q: You can use MATLAB to simplify the answer,just screenshot the matlab process

A: We are to find invertible matrix P so that J=P-1AP is in jordan canonical form. We will find P, J…

Q: Find the basis of the null space of the matrix 1. A = 2 -1 3 6 6 -2 (a) , (b) (c) (d) d. a O b O…

A: Given - A = 12-136-2 To find - Find the basis of the null space of the matrix A.

Q: Diagonalizing a Matrix In Exercises 7-14, for each matrix A, find (if possible) a nonsingular matrix…

A: The given matrix is A=2-2   30   3-20-1   2 We have to find a nonsingular matrix P such that P-1AP…

Q: Find the rank of the following matrices.

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Q: Given the matrix 9. 6 -1 -5 -3 -4 A = 3 -6 -5 1 -3 Find an invertible matrix P so that J = P-AP is…

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Q: (470) Find the matrix A if A 1

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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: In Exercises 1-6, list the minor matrix Mij, and calcu- late the cofactor A¡j = (-1)i+j det(Mij) for…

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Q: A18.2 Let A be the matrix of rotation by /26. Write the matrix which is the inverse of A3 and…

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Q: |adjA| = |A]"=1 n-1

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

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Q: Verify that (a) AI=A (b) IA=A A 6 [Vo$₂2] 7 Part: 0 / 3 Part 1 of 3 Write the correct identity…

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Q: Let A, Be M, (C) be positive definite. Prove that (4+ B)" s(A" +B").

A: Let A,B∈Mnℂ be positibve definite.  To prove A+B-1≤14A-1+B-1 Since, A and B are positive definite,…

Q: Find an LU factorization of the matrix A. 3 5) A = 6 24 7 3 6 -5 22

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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…

A: Given; L=[[1,0,0],[-2,1,0],[-3,1,1]] and U=[[1,4,3],[0,2,6],[0,0,3]] .

Q: (4) Let A be a 3x3 matrix. If |4|= 2 , then |3.4|=,

A: Given that A be a 3*3 matrix and |A|=2. To find the value of |3A|

Q: Find the characteristic polynomial of the matrix -9 A = 1 p(z)

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Q: 3 1 Let A = 3 5 Find a basis with respect to which the linear transformation associated to the…

A: To find basis with respect to which the linear transformation associated to the matrix A would…

Q: 7. x1 4 -1 7 -4 + x2 -5 3 -5 1 + x3 7 -8 0 2 = 6 -8 0 -7

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Q: 5. X1 +х2 -3x1 + 2x3 х2 - 2х3 || 0 2

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Q: 15. -1 1 0 -2 3 -1

A: A=500-110-23-1

Q: (e) Suppose we just had the matrix A, but not the expression that was used to generate it. He we…

A: Suppose we just had the matrix A but not the expression that was used to generate it.

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: 17. Let A and B are similar matrices, that is, A = P-¹BP for some invertible matrix P. Then, prove…

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Q: Consider the matrices in Exercises 1–10. a) Either state that the matrix is in echelon form or use…

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Q: Determine the matrix A if (GA" – 21)* = 1.

A: Inverse matrix formula is A-1=1AAdjoint(A) Property in inverse (A-1)-1=A