UCSF 137 Lecture 8: UCSF 137 - Lecture 8 (2)

Given the matrix A = (1 -1 0 -1 2 0 0 0 3), find an orthogonal matrix H such that H^T AH = (3 + Squareroot 5/2 0 0 0 3 0 0 0 3 - Squareroot 5/2).

The vector is in the set. What value of the parameters produces that vector? (5 -5), {(1 -1)k |k epsilon R|} (-1 2 1), {(-2 1 0)i + (3 0 1)j |i, j epsilon R|} (0 -4 2), {(1 1 0)m + (2 0 1)n |m, n epsilon R|} Decide if the vector is in the set. (3 -1), {(-6 2)k|k epsilon R} (5 4), {(5 -4)j|j epsilon R} (2 1 -1), {(0 3 -7) + (1 -1 3)r |r epsilon R} (1 0 1), {(2 0 1)j + (-3 -1 1)k |j, k epsilon R}