4. Upper Triangularizalion In this problem. you need to upper-triangulat'ize the matrix 3 1 2 A = 3 1 E 2 2 2 The eigenvalues of this matrix A are A1 = A2 = 2 and Jig = 4. We want to express A as where the 4}: Ease orthonormal. Your goal in this problem is to compute 137,2 so that theyr satisfy the above relationship for some constants c? II? c. Here are some potentially usetl facts that we have gathered to save you some computations, you'll have to grind out the rest yourself. 3 1 2 J5 3 _1 6 = as. 2 2 2 [1 Wealsoknowthat a g u E 1' 2 1' 2 s I] [l isanordtonormalhasis,and vi mg no U 3 '1 9 s U n has 3 2 . 3 1 El . _J I] = . U U 1 [)2 1 _2,y" _2 2v' We also know that _2 _2 has eigenvalues 2 and 4. The normalized eigenveetor corresponding _ e s tth=2is |: g] and [g] isaveotorthatisorthogonaltothatandalsohas norm 1. Based on the above information, compute :E. g}. E. Show your work. You don't have to compute the constants c, b, e in the interests of time