Problem 7. [23 Let A-8 11 -16. Find an orthogonal matrix P with rational entries and a diagonal matrix D such that D = PT AP. -8-16 11 -2 -2 P = 1 1 1 0 0 D= 27 0 0 27

Q: 7. Consider the two matrices A and B write an elementary matrix E such that B = EA -2 3 8 A = [5, 3²…

A: Solution : Given that

Q: If u = and , then what is the magnitude of 2 + . Round to the nearest hundredth. Answer:

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Q: 1 2 5 -3 Find a matrix X that satisfies XA=B, where A = and B = 2 5 3 -5

A: We find inverse of A then fin matrix X.

Q: -14 2 4 Let A= 2 -17 2 Find an orthogonal matrix P with rational entries and a diagonal matrix D…

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Q: Show that D^2 = {(x, y) ∈ E^2: x^2+y^2 ≤ 1} ⊂ E^2 and the space containing a single point are…

A: In algebraic topology, two topological spaces are said to be homotopy equivalent if there exists a…

Q: 19. Given the augmented matrix 1 4 -2 1 R2 = r2 – 7r, R3 = r3 + 2r, 7 29 -15 -2 -6 7 19 Perform the…

A: INTRODUCTION: A matrix is a collection of numbers that are arranged in rows and columns to form a…

Q: . One might need to find solutions of Ax = b for several different b’s, say bị, ., bỵ. In this…

A: first we will reduce the multi augmented matrix into reduced echelon form (rref) then find the…

Q: ) Suppose A = 1 and B is a 2 x 2 matrix with det (B) = -12. Find det(-3A²B-¹).

A: The given matrix is; A=[4 -1     -2   1]det(B)=-12Find det(-3A2B-1).

Q: -3 29 17 -3 -2 x-24 8-17] 1--15 23 12 2--16 0 Y = Z 9 -5 -2 12 9 -1 9 W=-11 15 = 8 -20 ID H YTOV >>>…

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Q: 17. Let [12 A¹ = 0 3 1 412 If possible, find a matrix C such that --- ACA = 2 1 3] 2 2 214 -1

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Q: 10. Consider the following matrices: A = 13 0 1 3-5 1]. B A² BA CA DA 10-1 215 -3 4], C-[|-||---|| 0…

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Q: compute the indicated matrices AB

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Q: If A, B, and C are 3×3 matrices; and det(A) = -1, det(B) = 4, and det(C) = 3 then compute:…

A: We know properties of determinant for n×n matrices A, B…

Q: 4 Apply the Cholesky factorization to A = -2 4 A = UTU. U = lo 10 x1 16 Solve A x2 = -88 by first…

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