Consider the following. (a) Compute the characteristic polynomial of A. det(A - AI) = -2³ +72² +172 +9 A₁ = A = (b) Compute the eigenvalues and bases of the corresponding eigenspaces of A. (Repeated eigenvalues should be entered repeatedly with the same eigenspaces.) ^₂ = 4 05 6-1 6 5 04 23 = has eigenspace span has eigenspace span has eigenspace span ↓↑ (c) Compute the algebraic and geometric multiplicity of each eigenvalue. A₁ has algebraic multiplicity and geometric multiplicity ₂ has algebraic multiplicity and geometric multiplicity 13 has algebraic multiplicity and geometric multiplicity (smallest λ-value) (largest λ-value)

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

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Q: Calculate the characteristic polynomial of the following matrix A, and use it to compute eigenvalues…

A: We find characteristic polynomial and eigenvalues of A.

Q: Find all eigenvalues with their algebraic multiplicities. -1 0-2 0 -3 0 -4 3 1 Let X₁ and X₂ be the…

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Q: λι = From smallest to largest, the eigenvalues are ₁ <₂<3 where 2₂ 3 23 = Find the eigenvalues and…

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Q: [1 0 0 A = |1 0 -2 |1 1 2 (a) Find all of the (possibly complex) eigenvalues for A. (» Without…

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Q: Let A = 3 −1 0 0 −1 T300 003 T −1 0 0 -1 3 (a) Find the characteristic polynomial of A. (b) Find the…

A: Introduction: The characteristic polynomial of A is defined as function  and the characteristic…

Q: ab. A-1 -1 5 -5 AXI= 사 5 -5 = 저 - 5 -5-7 det(A-xz)=(지(5-2) - (-1)(5) a = 2² +62 +5 +5 = 2² +67+10…

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Q: [001] 0 0 1 0 A = 1 0 nd the characteristic polynomial and all eigenvalues, both real and complex.…

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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: Can step 2 be more elaborated upon? Specifically on how each eigenspace is found.

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Q: Compute an eigenvector for 9 3 1) corresponding to the eigenvalue of 7.

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Q: if \phi 1(x) and \phi 2(x) are two normalized eigen functions and \phi (x) = c1\phi 1(x) + c2\phi…

A: If ϕ1(x) and ϕ2(x) are two normalized eigen functions and ϕ(x)=c1ϕ1(x)+c2ϕ2(x) is also a normalized…

Q: Suppose a certain 4 x 4 matrix A has two distinct real eigenvalues. What could the algebraic…

A: Let A be a 4×4 matrix with two distinct eigenvalues λ1 and λ2 having algebraic multiplicities n1 and…

Q: 2 -1 -1 4 -1 1 2 = 1 -1 0 -1 -1 - 0 −1 1 30 020 03 10 0 ㅜㅜㅜ -1 -1 -1 -1 0

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Q: 2 1 -1 -1 4 -1 1 2 = 1 -1 0 -1 1 -1 0 -1 1 300 0 -1 -1 020 -1 −1 −1 003 -1 -1 0

A: if a matrix A is diagonalized it can be written as  A=PDP-1 where D is the diagonal matrix formed by…

Q: For 2 = -1, we found the eigenspace consists of solutions to the following. 20 2 0 0 0 0 0 0 0 0 0…

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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.