Problem 7 Let 2 0 0 A = 0 1 0 1 2 (i) Determine the eigenvalues and eigenvectors of A. (ii) Explain why the collection of basis vectors of the eigenspaces form a basis for R³. (iii) What are the eigenvalues and their corresponding eigenvectors of the matrix A – 2A? – 3A +I.

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Q: Hi, could you help me find the eigenvalues and eigenvectors of this matrix,

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Q: Let's now find the corresponding eigenvectors: Plugging in a₁: Plugging in a2: 0 1 (9) 0 - 0 - λ 1 0…

A: The given matrix is 010100002. To Find: Corresponding eigenvectors.

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A: for ease of everything I will provide whole answer.

Q: Solve for all the eigenvectors.

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Q: 4) Eigen valves and eigenvectors Let's say A = 5 3 %3D A-AI = ]- 5. %3D 3. 5-2 L 30 ニ Quadratic…

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Q: 即 -2 0 1 E). EL 0 亦 2 心→ I I - 一1

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Q: I want to find the eigenvalues for the matrix   8-x   -6   2 -6   7-x  -4 2     -4     3-x…

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A: Given matrix  C  is ,                                                            C =4   14-70-10…

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Q: 4 3 -3 +---)-(6) --- 00 0 12 0 A-1 = 120 A-21= 0 5 3 0 0 0 3 3 -3 -(6)-( 0 -1 0 1 2 -1 1 0 0 1 0 0 0…

A: ⇒A-I=43-3000120 ⇒A-2I=33-30-1012-1 ⇒A-4I=13-30-3012-3

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Q: Therefore, the roots are, r₁ = 1, r2 = -1. Substitute r 1 in the system. www 1 -1 () ()-() = 3 -3…

A: How do you get to the reduced form and then get the eigen vector in this problem?

Q: Solve this question on Matrix

A: ( If you have any queries please feel free to ask me).

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Q: The trace and determinant of a 2 x 2 matrix are known to be -2 and -35 respectively. Its eigenvalues

A: solution :given that trace=-2and determinant =-35 of a 2×2 matrix .we know that trace =…