Question 11 5 The sets en NN contains a basis for R4. Find a basis for...
7 -4 8 Consider the 3x3 matrix A= 4 -1 8 -4 4 - 5 (a) Find the eigenvalues of A. Show every step of your work. The key to successful factorization is not to distribute anything in the determinant until you have factored out everything you possibly can from all terms. When your factorization is complete, it should show the algebraic multiplicity of each eigenvalue. (b) What is/are the eigenvector(s) corresponding to each eigenvalue? (c) What are the eigenspaces?
Question 11: 0 5 3 0 2 The set Sa contains a basis for R4. Find a basis for R4 -3 -1 12 -3 9 2. 5 consisting of vectors from S.
Tk 1 21 5 -5 k (a) Find the determinant of A in terms of k (b) For which value(s) of k is the matrix A invertible? (c) Let B-(k,1,2,0), (0, k, 2,0),(5,-5, k,0)) be a set of vectors in R4, and let k equal some answer you gave for part (b) of this question. Add an appropriate number of vectors to B so that the resulting set is a basis for R'
Tk 1 21 5 -5 k (a)...
Question 4
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