(b) Find all the values of λ such that matrix B is a singular matrix. 1 λ λ2 1 1 B = 1 3 1 9

Q: Find an invertible matrix P and a matrix C of form that A PCP-¹. = P = C = −2+ i -2- i 2 2 3+2 i 0…

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Q: A? 0 0 A =

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Q: Let A = [ 9-8 4-3 Find an invertible matrix X such that X-¹AX is diagonal.

A: Introduction: A matrix A of dimension n x n is called invertible if and only if there exists…

Q: -4 -4 4 M = 12 15 -14 -35 + k -27 26

A: The given matrix is  M=-4-441215-14-35+k-2726 If the determinant of the matrix is zero then the…

Q: Let A = [5 0 X = 5 Find an invertible matrix X and a diagonal matrix D such that X-¹AX = D. 001 D =…

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Q: 32x+y -1 526 -1 x+4y 10

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Q: Use elementary row operations to determine A-1 (you should be able to do (a) elementary row…

A: 1.a A=123-111201A=11-0-2-1-2+30-2     =1+6-6     =1determinant of A is not zero, therefore inverse…

Q: Find the characteristics roots of the matrix 2 A =| 1 2. 2.

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Q: Let a be a real number. Let 1 1 A = | 0 1 1 1 1 2 a) Find the value of a for which the matrix is not…

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Q: Orthogonally diagonalizable the following matrix 2 1 1 C = -1 1 1 0 -1 1.

A: The solution is below.

Q: Determine all the n × n− matrix A with the range such that A2 = A.

A: Clearly the zero matrix and identity matrix are the trivial examples of our problems. However there…

Q: Find all real numbers a, b for which the matrix A nalizable in R. = ( 1] is diago-

A: We have to find all real numbers  for which the matrix  is diagonalizable in

Q: Find a 3 x 3 matrix A such that A A A A = 1 4 0 = 2 0 -1 B-B EL. 0 2 1 = -3 and 0 -5 0 -5 B-B 0 -5 1…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Let 4 1 -2 2 1 A = 1 -2 0 3 -2 2 1 -2 -1, Use Householder method to transform A into a tridiagonal…

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Q: real matrix which is not diagonal. If (A + I)² = 0,

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Q: P = ) Let A = -15 -8 -8 0 -3 0 24 16 13 Find an invertible matrix P and a diagonal matrix D such…

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Q: Let -1 1 A = -1 1 -1 -3 3 Find an upper triangular matrix which is orthogonally similar to A.

A: An upper triangular matrix is a triangular matrix with all elements equal to below the main…

Q: Consider the matrix B given by 0 0 0 B = 1 0 0 0 1 0 Show that B3 = 0. Also, compute for the product…

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Q: Solve the following equation involving a determinant. If y multiple answers, enter them as a list,…

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Q: Let A be the n × n matrix given by Show that det (A) = (a - 1) n − 1(a + n - 1)

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Q: 2 Consider the 3 × 3 matrix B = 1 2h -1 1 2 1

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