Question

Please solve the following linear algebra problem. Please do parts 1 and 2 and please show all work thank you.

Problem B. (4 pts) Consider the matrix 1 - / 2 1 1 1 2 1 - 1 -1 0 You can assume that = 1 and X = 2 are eigenvalues of the matrix A. (Note: You don't have to compute the eigenvalues of A.] 1. Find an eigenvector associated with = 1. 2. Find an eigenvector associated with A-2. Caution 1: Note that each eigenvalue must have an eigenvector, and the zero vector (0.0.0) can not be an eigenvector by definition. If you have obtained the vero vector as the only possible eigen vector, then there must be a computational error early on. If you claim, in your solution, that the zero vector (0.0.0) is an eigenvector associated with an eigenvalue, then you will receive no credit for the Problem B. Caution 2: During the row reduction process, you must indicate, at each step, which elementary row operation was performed. Also, make sure that you are using only the elementary row operations The use of nonelementary operations in the primary cause of computational errors. The operations R, +2R2 → R and Ry - Ry - Ry are NOT elententary row operations. Similarly, 2R2 + R R , and - R + R2 - Rs are NOT elementary row operations. Note that the operations R: +2R, R2 and Ry - R R are elementary row operations. For further detail. please look over the Unit I note. 710

Answer 1

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So X3 Choote х- Eigen Vecdor X2 2 Associata K E1gen CAn Kto genral K K -2 Assocate to vector that veafy Eigen vector Fo an S AT=2X 2 2 1 (2-1 2 2.

Thank You !