MATH115 Study Guide - Quiz Guide: Diagonalizable Matrix, Diagonal Matrix, Linear Combination
2 Dec 2014
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Math 115 fall 2012 lab 7 solutions: {12 marks} consider the matrix a = For each eigenvalue, determine a basis for its corresponding eigenspace. We nd the characteristic polynomial to nd the eigenvalues. det(a i) = = ( 1 )( 2 2 3) So the three eigenvalues are = 1, 1, 3. Using x2 and x3 as our parameters, a basis for the eigenspace for = 1 is. A basis for the eigenspace for = 3 is. Using part (a), we can diagonalize a to d = that p 1ap = d. (c) use part (b) to determine a4. We see that a = p dp 1, and so. 0: {3 marks} determine a 2 2 matrix with eigenvalues 2 and 3 where corresponding to those eigenvalues respectively. We can diagonalize such a matrix a into d = (cid:20) 3 (cid:21)(cid:20) 2. 0 3 (cid:20) 2 (cid:21) (cid:21)(cid:20) 5 4.
