[2 1 4. Let A = 1 1 -1 2 -1 2 Show that the characteristic polynomial fa of A is -X³ + 5A² – 21 – 8. Note: fa factors as -(A – 4)(A – 2)(A + 1). You don't have to show this. 4 0 0 2 (b) Let D = Find an orthogonal matrix S so that A = SDS". 0 0 Express e in coordinates with respect to the columns of S.

Q: 2. Show that for any x, the matrix A = A² = I. [cos(2x) sin(2x) [sin(2x) − cos(2x)] - satisfies the…

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Q: + Y are invertible matrices of the same size, then X(X¹+Y-¹) Y(X+Y)-¹ = 1.

A: One has to show the said property.

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Q: Q4. Find the singular value decomposition of the matrix A this to find the SVD of the matrix (ATA)-2…

A: Given matrix is Then,

Q: 5.1 Pr 5.2 Use Theorem 5.3(h) to find the Moore-Penrose inverse of [1 1 1 1 A = 1 1 2 0 1 Theorem…

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Q: Let B = {(1, 1), (2, 3)} and B′ = {(5, 2), (1, 3)} be two bases for R2. [T]B= 2 3 4 7 (a) Find (T…

A: please see the next step for solution

Q: 2. For the matrix 2 2 -1 B -3 3 find its Pseduoinverse Bt and the 2-norm ||B*||2.

A: Given : B=212-1-1-3-13 To find : pseudoinverse B+ and the 2-norm ∥B+∥2

Q: - Let p(t) = t5 - 6tª + 6t3 – 6t² + 5t. a) Factorise p(t) as a product of degree 1 polynomials. b)…

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Q: 1 2 2 1 -2 1 . Find the characteristic polynomial A4(t) for the matrix A -3 2 -1

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Q: Which of the following matrices have characterestic polynomial p(W) =12 – 10A + 1 Select one: а. 1 1…

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A: As per Bartleby Instructions only first three can solved. Upload others separately. a. Let f be a…

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A: To find:  and

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A: Given matrix is A = -5-2005-1-2-30

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A: Note: - Since you have asked multiple question, we will solve the first question for you. If you…

Q: -3 Given matrices A-B and B- and B= , verify that det (AB)= det(A). det(B). Find the third Taylor's…

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Q: 4 8. 5. Let C = 0. the cofactor matrix of a matrix A and let 7. -7 9] 611 b12 b13 A the inverse…

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A: To express the characteristic polynomial of A^2 in terms of the characteristic polynomial of A

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