1
answer
0
watching
48
views
10 Nov 2019
4. Let 1 0-1 2 3 1 A--1 3 02 2 2 2 2 5 -2 3 0 2 -2 6 (a) [10 marks] Define and compute the I1 operator norm of A. (b) [7 marks] Prove that any eigenvalues of A are real. (c) [8 marks] Prove that any eigenvectors of A corresponding to different eigenvalues are orthogonal to each other (in the standard, Euclidean inner product) Hint: (b) and (c) can be answered without computing explicitly the eigenvalues/eigenvec- tors of A. In fact, you only need to use one property of A, which can be easily checked. Total: 25 marks
4. Let 1 0-1 2 3 1 A--1 3 02 2 2 2 2 5 -2 3 0 2 -2 6 (a) [10 marks] Define and compute the I1 operator norm of A. (b) [7 marks] Prove that any eigenvalues of A are real. (c) [8 marks] Prove that any eigenvectors of A corresponding to different eigenvalues are orthogonal to each other (in the standard, Euclidean inner product) Hint: (b) and (c) can be answered without computing explicitly the eigenvalues/eigenvec- tors of A. In fact, you only need to use one property of A, which can be easily checked. Total: 25 marks
Collen VonLv2
16 Mar 2019