V. Let T and Q be the matrices -2 -1 -9 -5 -2 0-1 -8 -2 3 -4 T = Q = 2 3. 11 -2 3 -5 -13 -7 3 -1 -4 3 1. Explain why the columns of Q are a basis for R'. 2. Verify that X = span (Q.1.Q.2) and y = span (Q.a. Q.4) are each invariant subspaces under T. 3. Compute the product Q-TQ to determine 4. Judge if T is diagonalizable. If so, find a nonsingular matrix P such that P-TP is diagonal. If not, explain in detail.

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Q: find A*B and B*A for the matrices A= 10 1 2 1 1 3 2 -1 B= 0 0 3 1 2 4 -1 -1 0

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Q: 1 Find the linear combination 2$1 +382 + 4s3 b. Then write b as a matrix-vector multiplication Sx.…

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Q: .

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Q: 5. Consider the vectors u 11. and y= a. Use row operations on an augmented coefficient matrix to…

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