## Question

###### V(atvxCousider thc lincar opcrators Tla +br) = (2a b) + 2br and Utr b) = (2a +6) + (a + 26)1 ou P(R).Find the cigenvalues of T anud U. [12 points] Find basis for the cigcnspaccs corresponding to thc eigenvalucs of T. [4 point] (c) Find basis for thc cigenspaccs corrcsponding to the cigenvalues of U_ [8 points] Is T diagonalizable? If $0, find basis 8 such that (Tla is & diagonal matrix_ and find [Tla. IF uot , cxplain why: [2 points] Is U diagonalizable? If s0, find basis 6 such that [Ul

V(atvx Cousider thc lincar opcrators Tla +br) = (2a b) + 2br and Utr b) = (2a +6) + (a + 26)1 ou P(R). Find the cigenvalues of T anud U. [12 points] Find basis for the cigcnspaccs corresponding to thc eigenvalucs of T. [4 point] (c) Find basis for thc cigenspaccs corrcsponding to the cigenvalues of U_ [8 points] Is T diagonalizable? If $0, find basis 8 such that (Tla is & diagonal matrix_ and find [Tla. IF uot , cxplain why: [2 points] Is U diagonalizable? If s0, find basis 6 such that [Ul: is & diagonal matrix, and find [Ule . If uot, explain why: [3 points]

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