Question 1 Consider the matrix 4 5 0 1 0 -7 7 3 A = a) Determine all eigenvalues and eigenvectors. Then, find the ma such that D = P-lAP. b) Determine Dk then deduce Ak.

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Q: ak + b) {{} = m – 1). k=0

A: Please cheek the details in the next step

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Q: Question 3 Compute the eigenvalues and eigenvectors of the matrices A and A-1 4 A = V3 V3 2

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Q: 3. S (x +) dx

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Q: 5. L' s+7 s(s – 3s –10)

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Q: Given r(t) = (sin t - t cost)i + (cost +t sin t)j + tk , find the unit binormal vector and torsion.

A: Unit binomial vector  b=r'×r''r'×r'' torsion  τ=(r'×r'')⋅r'''r'×r''2

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A: Solution 

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