MAT 310 Final: MAT 310 SBU Fall12 Final Odd Numbers
31 Jan 2019
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Document Summary
Solution 0. 1 (problem 1) you should take this problem as a list of de nitions you should know. Consult the book if you don"t know it. Solution 0. 2 (problem 3) in matrix form, the problem is nding x in: Solution 0. 3 (problem 5) p 2 = p tells us the eigen values of p are all 1 or the vector is in the kernel. Contradicting ej being an eigen-vector: true - assuming the book allows eigen values to be zero, true - conjugate by the matrix s which sends the eigen vectors of one to the eigen vectors of the other. Solution 0. 5 (problem 9) diagonalize s and split the vector space into eigen spaces w . Commutativity implies that the sub space w is spanned by the eigen-vectors of s with eigen-value are preserved by t : This follow from: sv = v s(t v) = t v.
