4 1 3 0 6. Let A = -1 2 0 4 1 2 (a) calculate determinants.) Find the characteristic polynomial of A. (Feel free to use WolframAlpha to (b) WolframAlpha to help factor the characteristic polynomial.) Find all eigenvalues of A and their algebraic multiplicities. (You may use (c) For each eigenvalue of A, find a basis for the corresponding eigenspace. (d) If possible, diagonalize A; if this is not possible, then explain why not.

Q: For Matrix A, find a basis for the eigenspace corresponding to λ = 3. 4 A = 3 0 0 2 2 - - 1 3 5

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Q: Consider the operator R2 → R2 given by left-multiplication by the matrix: A =[−2 −1,        1 −4].…

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Q: , a linear operator and a scalar λ are given. Show that is an eigenvalue of the operator and…

A: Given linear transformation…

Q: - Let p(t) = t5 - 6tª + 6t3 – 6t² + 5t. a) Factorise p(t) as a product of degree 1 polynomials. b)…

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Q: Find a basis for the eigenspace of B below. 2 1 B = 0 3 a. B= ((0,1),(1,0)} b. B= ((- 1,0),(1,1)} B…

A: To find the Basis for eigen space , first I have to find the eigen values then find the eigen vector…

Q: X2 X₁ + X₂ x2 64-B be bases for R2 and R³, respectively. (a) Compute MȚ(B, B'), the matrix of T with…

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Q: 5. For each linear operator T on V, find the eigenvalues of T and an ordered basis for V such that…

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Q: 1 0 0 cos 0 sin i. Find the inverse of R. Show that R= 0 sin o cos is orthogonal. ii. Find the…

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Q: [1 2 8. Let A = and define Q : R² → R by Q(x) = x"Ax. 2 1 (a) Find the characteristic polynomial of…

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Q: , a linear operator and a scalar λ are given. Show that is an eigenvalue of the operator and…

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Q: 1. -2 -2 Let A = -2 -2 -2 -2 1 Determine the characteristic polynomial of A: I-1 2 XA(x) = det(rI3 –…

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Q: a b Let A = cd We have defined the determinant of A: det(A) = A = ad - bc. There is another quantity…

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Q: Find the change of basis matrix [] and use it to find [v].Ⓡ. B B 0 {Q[C])} 4 [V] B 0.5 -0.5 1.5 1 16…

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Q: Prove that if A is an eigenvalue of the n x n matrix A, then is also an eigenvalue of AT.

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Q: Example: Let S = span -{0-0} 3 1. Why is -1 € S? -1 2. Why is -1 inS? 3 3. Is 0€ S?

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Q: -3 Given matrices A-B and B- and B= , verify that det (AB)= det(A). det(B). Find the third Taylor's…

A: (i)

Q: [2x + y] [x – E) = - 3l: (Show all work in this problem.) a. Find the matrix of F with respect to…

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Q: The given T is a linear transformation from R2 into R². Show that T is invertible and find a formula…

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Q: Find the characteristic polynomial of the matrix, using either a cofactor expansion or the special…

A: We find the characteristic polynomial of the given matrix why using cofactor expansion.

Q: The given T is a linear transformation from R² into R². Show that T is invertible and find a formula…

A: Hence T is invertible.

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Q: Find the change of basis matrix from G to H. - {[::}[::} [} 6 1 25 5 2 3 1 0 1 1 0 0 0 0 G = H = 0 0…

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Q: 1. Answer the following for A = b. Find a basis for the eigenspaces. 1 -3 3 3 3 -5 -3 3 1 ننا ننا

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Q: Let B = {x²+x,-2x² + 3x + 3, 2x² – x – 2} be a basis of P2(R)

A: Given,            B=x2+x,  -2x2+3x+3,  2x2-x-2