P = Let A -38 70 105 7 15. Find an invertible matrix P and a diagonal matrix D such that D = P-¹AP. 20 27 -5 -10 D

Q: Given a matrix A = -2 Find the matrix B if 2B - 312 = A. %3D

A: Given: A= 50-21 Now lets assume B=abcd

Q: For which values of the constants b and c is the follow- ing matrix invertible? 1 b -1 -b

A: The given matrix is 01b-10c-b-c0

Q: [2 -1 1] A = |1 1 2,x = |y| and b = |b2 [-1 5 4] a. Determine if the columns of the matrix A span…

A: We have to determine  whether the column of matrix A can span R^3

Q: -2 6. What is the diagonal matrix Find an orthogonal matrix Q that diagonalizes A = 6. A?

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Q: Find the matrix A if 3 1 4 A = 11 00

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Q: Diagonalize the given matrix A and hence find A². 10 -2 -5] 2 3 3 5 A = -2 -5

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Q: matrix P and a matrix C of the form -21 a -b b ces P and Care mma to separate answers as needed.) no…

A: Let    Given that Eigenvalues of A are 5+2I and 5-2i With corresponding eigenvectors are 2+2i-i And…

Q: Determine if the matrix is nonsingular. Explain. [1 3 21 1 4 l1 -7 21

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Q: Create two 2 x 2 matrices A and B, to show that (A+ B) - A+B is not always true. Clearly write A, B,…

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Q: ; = \57 -77 -80/ В — 42 72 75 4 288 -82 -1 4 а. Find B-1

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Q: Diagonalize the following matrix. – 26 – 15 50 29 D 1 P ||

A: Let A=-26-155029. To diagonalize the matrix A, first we have to find the eigenvalues of the matrix…

Q: 1 31 A = 2 7 . A·B = B · A = I3×3 -2 -4 -5. ]

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Q: a 3 A= -6 2 2 4

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Q: Let's create a matrix that reflects around a line that is perpendicular to the vector n = [0.375,…

A: A matrix that reflects around a line y=mx s given by, 1-m21+m22m1+m22m1+m2-1-m21+m2 Since, the line…

Q: -3 -1 Find all a so that the matrix A = 1 -1 is positive -1 4

A: Matrix A is position if and only if all of the leading principal minors are positive.    Then follow…

Q: -1 2 аnd AB 5 1. Find the matrix B. 3 Let A = 6 -9

A: This is a problem of matrix multiplication. Based on the general formula we will solve the question.

Q: Diagonalize the following matrix. – 13 - 42 5 16 %3D D P-1 =

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Q: Find the transpose of the matrix. 4 5. D = -2 -1 -3

A: The transpose of a matrix can be  found by interchanging its rows into columns or columns into rows.…

Q: -16 8 20 In other words, find an -40 invertible matrix P and a diagonal matrix D so that A = PDP-¹.…

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Q: -6 7 3 Let A = -5 6 3 Find an 5 -7 -4 invertible matrix P and a diagonal matrix D such that D =…

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Q: Find the matrix A such that 10 [-13]4 ;]₁ = [ A -1 3 Hint: Let A = A = a b [26] d -1 -5 2 8

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Q: 3. Find m and n so that the matrix below is symmetric:

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Q: Linear Algebra 3 Find the projection of 6 (4,3,1,0) onto the row space of the matrix -1 -1 0

A: The projection of X on Y matrix is : X^=XYTYYT-1Y........1 let b→=X and A=Y X=4310Y=1111-2-102…

Q: 0 13 3. Find the matrix A such that A -6-20 use the variables a,b, c, d for the entries of A. 2-2…

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Q: Find R = A + B, given that A has magnitude 4 and is at an angle of 30° above the positive x-axis and…

A: Let a vector be defined as: a=x, y. The magnitude of a is calculated using the formula: r=x2+y2.…

Q: N.N て1 て てー -3 こ 1. そー ) Find oenk of the matrix p

A: See the attachment

Q: Diagonalize the matrix 4. -3 A = 3 -1 1 -2 3 2 by finding a nonsingular matrix S and a diagonal…

A: Given: A=4-3-33-2-3-112To find the characteristic polynomial :…