(2 0 2 Consider the matrix A = 0 2 1. Find a Jordan matrix J and an 1 -2 0, invertible matrix Q such that A = QJQ¯'.

Q: 1 a) For the matrix A 1 3 1 find an orthogonal matrixQ such that 1 D =Q AQ is a diagonal matrix.…

A: We will find Eigenvectors to solve the problem.

Q: 2. Find a vector orthogonal to the nullspace of the matrix [1 27 6. 4 L5 -1 2.

A: According to the given information it is required to find a vector orthogonal to the null space of a…

Q: 3(4) 5 A = %3D -1 2

A: Here in the given question find the canonical form of the matrix A, which is P-1 A P = B   Find the…

Q: Q2: (a) For given matrix A, find a 3 x 3 non-singular matrix P such that p-1AP is diagonal. A = |-3…

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Q: 6. 5 X•W Compute x using the vectors w = -2 and x =| - 2 - 3 2 (Simplify your answer. Type an…

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Q: Find the RREF of the matrix -4 1 -3 من که من 2 3 -1 4 -2 3 2

A: to find the row reduced echelon form of -4       31      - 1-3       42       - 23        2

Q: Find a matrix A such that e [-] -2 is a solution for Ax= x'.

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Q: (2 0 0 2. Let A = |1 2 -1 \1 3 -2, Determine a matrix P such that P-1AP is diagonal matrix D and…

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Q: A) Justify if the matrix A is diagonalizable.B) Find a matrix T and a diagonal matrix J, such that…

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Q: * For the matrix A, find det A 1. A = = | 3 -2 1 [2 |1 -1. det A = 25 O det A = -2 O det A = 1 O det…

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Q: (3) Suppose that A and B are 4 x 4 matrices and that det(A) det(B) = Then %3D det(-A'BA"…

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Q: 2.3 Explain how you obtain the matrix N that rotates a point 180° anticlockwise around the point…

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Q: 4. Let A be an n x n matrix such that A31 = 0n. (a) Show that In - A is invertible. (b) Let B be an…

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Q: [1 0 [9 0 01 c) A-2 = |0 4 0 Lo o 1l 9. Find a matrix A that satisfies a) (3.4) =0 -1 1 |0 0 -1| 2.

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Q: If A is an orthogonal matrix, then which of the following is true i. A has orthonormal rows A is…

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Q: det(cA) = c det(A) Insert a number to sho

A: Given that  A is an n×n matrix and c is a scalar. Check whether detcA=cdetA is true or false.

Q: 3 -4 Let the matrix A = be given. 2 -3 (f) If exists, try to compute a diagonal matrix similar to A.…

A: Given:                     A = 3-42-3. Here,                       (f) we have to find the diagonal…

Q: 1 Less positive Consider a symmetric positive definite matrix A separated into subblocks according…

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Q: (4) the matrix expression ABT - (CA-!)T is defined, then only one of the following is a necessary…

A: Q.4

Q: Determine it A= 0 3 2 diagonalizable. is 3о9 If find X such that X-'AX=D is diag onal matrux. yes,…

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Q: Q2/ Using Orthogonal Matrix 1 4 7, -8 4 If A = 4 prove that A- = A', A' being the transpose of A. 1

A: Solve by using the definition of the orthogonal matrix.

Q: Let 2 -1 A = 1 -1 0 2 Find an orthogonal matrix P and a diagonal matrix D such thatt D = P"AP. D =…

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Q: 1 4 [-1 Form the Matrix Ak? 3.Let Matrix A = 2 3 and k be any scalar b = -4. -3]

A: We need to find Ak.

Q: (c) For the real symmetric matrix A, find a non-singular matrix P such that PTAP is diagonal and…

A: Given: A matrix defined as .Aim: To determine the matrix , such that is a diagonal matrix. Also…

Q: 2 3 1 2 and B = 2 3 0 5 [1 2-2: Let A = |1 1 |2 1 3 a) Find A-B", if exists. b) Find the matrix C…

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Q: 2 0 and Y = (1 1 - Find the matrix z7 where Y = X-z X = 0 1 0 0 -2 I 1)=,

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Q: ₁ = [ 11, 11] Find a nonsingular matrix P such that PAP is diagonal where A = -5 P = = [00] OP - [3…

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Q: 2. Assume that A is a 3 × 3 matrix such that for 1 - (³).. ), j = 2 1 I 0 ;). it holds that Az = (a)…

A: Introduction: If the transpose of a square matrix with real numbers or elements equals the inverse…

Q: (2) Suppose A = (a) Diagonalize A (find an invertible matrix Pand a diagonal matrix D such that A =…

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Q: 9. (a) Let A = 0 3 5. Find an invertible matrix P, and a diagonal LO 0 41 matrix D, such that P-¹ AP…

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Q: (2a, Let A be a 3 × 3 matrix b b a A = a a a a a Show that A is invertible if a +0 and a + b. (2b,…

A: We need to prove and find value of c

Q: (BH) Recall that a matrix Q is orthogonal if Q' Q = I.

A: Given, A matrix Q is orthogonal if QTQ=I Proof: (a) The one way to write the norm for vector x is…

Q: 14. (a) Construct a 3 x 3 nonzero matrix A such that the vector Ax = 0. H is a solution of (b) If…

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