Let A be a 2 x 2 matrix with real entries. You are given that 6 – 3i is an 1- 3i eigenvalue of A with an associated eigenvector Use this information 1 a such that to find an invertible matrix P and a matrix C of the form a a11 a12 A = PCP¯1 If A = then the value of a11 is a21 a22

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Q: 12+3i 1) A = 7+4i -12- 6i -5-7i -1+i 3-i a) This matrix is diagonalizable b) The P matrix would be…

A: Given: A=12+3i-12-6i10+4i7+4i-5-7i7+4i-1+i3-i1 The eigenvalues of A are λ=2-i, 2-3i, 4.

Q: The matrix A is a real symmetric 5 × 5 matrix with eigenvalues 2, 6, 11, 14, and 19. The vector æ1…

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Q: 1 3 - Q5. Let A be the 2 × 2 matrix 1 1 (a) Find an eigenbasis B for A. (b) Find the B-matrix for A.…

A: As your question contains multiple subpart, so I only first 3 subparts.

Q: For the matrix A, find (if possible) a nonsingular matrix P such that P-¹AP is diagonal_ 2-2 3 0 3…

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Q: Suppose matrix A as follows: 2 -17 3 -2 0 ^ = [2 -1 a. Find the eigenvalues and eigenvectors of the…

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Q: Let. A be an eigenvalue of an n x n matrix A. Show that. 1² -3 is an eigenvalue of 31

A: Given :  λ is an eigen value of an n×nmatrix  A . We have to prove that  λ2-3 is an eigen value of…

Q: Show that if A has n linearly independent eigenvectors, then so does A¹.

A: We have to show if Ahas n Linearly independent eigenvector  then so does AT

Q: 0 Let V₁ = 2 and V₂ = Let v = -3v₁ + 2v₂. Find Av. Av= -2 be eigenvectors of the matrix A which…

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