[2 0 -2] 3. Let A = |1 3 0 0 3 (a) Find the characteristic polynomial of A and give the eigenvalues of A. (b) Find a basis for the eigenspace corresponding to each of the eigenvalues that you found in (a). (c) Using (a) and (b) find a matrix P and matrix D such that A = PDP-'.

Q: Eigenvalues 11 = 1 and 12 = -2 and their corresponding eigenvectors p1 =(1,2) and v2 = (3.7) Find…

A: We have to find matrix whose eigen values and eigenvectors are given.

Q: Suppose that a matrix A has characteristic polynomial p(^) = 24 − 3a³ + 82² – 24. Consider the…

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Q: Find a linear transformation I having 1₁ = 1 As an an eigenvalue associated to the vector (1₁ 1₁0)…

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Q: Compute the characteristic polynomial of 16 17 and use it to get the eigenvalues.

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Q: 2. If Verify that A = -2 (²3) B = (2²¹) c= (²¹) C 1) 0 2 (a) (A + B) + C = A + (B+C). (b) (AB)C=…

A: Hint: Solve RHS and LHS to varify all the three parts.

Q: Verify that 2, is an eigenvalue of A and that x, is a corresponding eigenvector. -4 -2 = -11, x, =…

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Q: Let u be randomly chosen vector in R³. Set and for k> 0 set 20 |||v|| ' A-¹æk ||A-¹æk||' Xo = xo…

A: We are given that A is a 3 x 3 matrix having eigenvalues λ1=-6, λ2=-2, and λ3=5. We are given the…

Q: [3 2 0] s) Consider the quadratic form Q(x) = x" Ax, where A = 2 2 2 0 2 1 (a) Given that vị = |2…

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Q: Let A = -1 -i a. Find the characteristic polynomial. b. Find the eigenvalues. c. Find the…

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Q: 1. (a) Determine the characteristic polynomial and eigenvalues for 0. A = |-1 1 -1 3 (b) Determine…

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Q: AX1 AX2 -4-2 3 1 СЕВЕ -2-7 6 2 1 2 6 -1 -4 -2 3 -2 -7 6 1 2-6 -4 -2 3 -2-7 6 1 2 6 Ax3 = 0 3 100 JT…

A: Here we have to verify that λi  is an eigenvalue of A and that xi is a corresponding eigenvector .

Q: 3. Determine the following for the matrix A. (a) Find the eigenvalues. (b) Find the bases of…

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Q: The symmetric matrix A below has eigenvalues −2 and 1 (multiplicity 2). Find an orthonormal basis B…

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Q: (c) Find f(A), where f(t) = tª – 4t3 + 3t – 7.

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Q: Exercise: Let A be an invertible n x n matrix. Suppose that u ER" is an eigenvector of A with…

A: For λ=2, u∈ℝn is an eigen vector of the matrix A and for λ=-7, v∈ℝn  is an eigen vector of A Note:…

Q: (3 5) 5. Let A 2 6 (a) Find the characteristic polynomial of A. (b) Find the eigenvalues of A.

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Q: The matrix T has eigenvalues and eigenvectors: • v = 1 with A =1. -1 1 with = 0. • V3 with A- Sive…

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Q: A = (; ) 5 -6 3 -4 (a). b) Find the eigenvalues and eigenvectors of A. Diagonalize A. (c) Find a…

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Q: Verify that 2, is an eigenvalue of A and that x, is a corresponding eigenvector. 2, = 5, x, = (1, 2,…

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Q: ues of M = 1

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Q: Suppose that A = a= b [0 a has eigenvalues -3 and 3. What are the values of a and b?

A: We have A=0a1b We find the eigen value by putting A-λI=0 Here, I=1001 Consider:…

Q: x(^) = x³ + X² +A+2 x(^) = x³ + x² +A+1 x(A) = X³ + 2A² + A + 1 x(^) = 1³ + A +1

A: This is a problem of stability and linear transformation.