1 0 0 0 X2 -2 -2 −1 2 0 1 00 2 −1 2

Q: (2) Determine all the real numbers a, b, c for which the matrix a 0 b 0 C is not diagonalizable.

A: The given problem is to determine for what values of a,b,c the matrix is not diagonalizable.

Q: a) Is A diagonalizable? Explain. b) If A is diagonalizable, rewrite A as XDX-1 (explain the choice…

A: a) Given            A=310010-310

Q: 3. Let 1 B -1 Consider T : R²,2 → R²2 defined by T(A) = AB – BA. Let - 이 [0 [o o] [o o] [1 0] Bị and…

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Q: c. Find an orthogonal diagonalization of the symmetric matrix 1 -2 0 A = -2 1 4

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Q: X = 4 1 -3 0 0 6 1 2 -12 10 -1 = [X₁ 5 X2 X3 X4]

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Q: Let 0 9. A = = [6 0 Is it possible to find a two by two real matrix B such that A = eB₂

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Q: Use the eigs () function to check the condition/structure of the XTX matrix

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Q: 1 1 1 0100 0120 00 0 Let A = Write A as C DC , where D is a diagonal matrix. Hint: You can always…

A: Given : matrix A=1110010001200000 We have to write A as CDC-1, where D is a diagonal matrix.

Q: Let A and B be two square matrices. Assume that both A and B are invertible. Show that BA is…

A: Note that--- If determinant of a matrix is non-zero then the matrix is said to be invertible and if…

Q: Consider the following (real, symmetric) matrix: A-(10 40 = 40 158 Determine the real canonical form…

A: Given:  A=104040158 To find the real canonical form of a given matrix.

Q: Let A be the following matrix: A = Find the scalar multiple –5A: 0 -3 2 3

A: The given problem is to find the scaler multiple of the given following matrix of A. Scalar multiple…

Q: Let A be an m × n matrix and r, s E R two scalars. Show the property that (r + s)A = rA + sA.

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Q: Determine whether the following matrix is diagonalizable or not. If yes, diagonalize it; if not,…

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Q: Set up the matrix which will perform the following transformation and write down its character. (x…

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Q: [121] In other words, write A = SDS-¹ = SDSt where D is a diagonal matrix and S is an isome- try.…

A:

Q: Suppose that the square matrix A is invertible. Show that the inverse of A is unique.

A: See below the explanation

Q: Suppose A is invertible.  Explain AT A is invertible.

A: The transpose of an invertible matrix is also invertible, and its inverse is the transpose of the…

Q: = 1 -2 2 00 0 -1 0 0 -1

A: Given that A=

Q: Determine for what real values a, b the following matrix is diagonalizable over the real numbers. a…

A: A matrix is diagonalizable if and only if for each eigenvalue the dimension of the eigenspace is…

Q: A. Construct a 2 × 2 matrix that is invertible but not diagonalizable. Also provide the inverse of…

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Q: Let A be a 2 × 2 real matrix. Determine conditions on the entries of A so that A2 = I2.

A: Given: Let A be a 2 x 2 real matrix.   To determine: The conditions on the entries of A so that A2 =…

Q: Show that if the matrix X is diagonalizable, then X" is also diagonalizable.

A: Given that the matrix X is diagonalizable. We have to show that XT is also diagonalizable. Since,…

Q: Find a non-zero 2 × 2 matrix A such that A2 = A =

A: We have to find a A matrix of 2x2 such that, A2  = 0000  So let suppose a matrix    Satisfy the…