3 Let v₁ = -3 and v2 = 2 be eigenvectors of the matrix A which correspond to the eigenvalues X1 1 0 Let v = -4v₁ + 2v₂. Find Av. -4 and X₂ = 2.

Q: 8 -3 0 7 9 2 -1 0 2 0 0 8 O O

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Q: and find the corresponding eigenvector.

A: λ is an eigen value if we have Av=λv for some v non-zero.v is called eigen vector.

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A: As per your request I have solved first subpart.

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A: See solution below.

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Q: Orthogonally diagonalize the matrix, giving an orthogonal matrix P and a diagonal matrix D. To save…

A: Our objective is given below:

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Q: Orthogonally diagonalize the matrix, giving an orthogonal matrix P and a diagonal matrix D. To save…

A: Given matrix,Let Now find the orthogonal matrix P and diagonal matrix D: