Q16.
Suppose T: R³ ? R³ is linear and has an upper-triangular matrix with respect
to the basis (1,0,0), (1, 1, 1), (1, 1, 2). Then, the orthonormal basis of R³ with
respect to which T has an upper-triangular matrix is
(1) (1,0,0), (0, $\frac{1}{\sqrt{2}}$, $-\frac{1}{\sqrt{2}}$), (0, $-\frac{1}{\sqrt{2}}$, $\frac{1}{\sqrt{2}}$)
(2) (1,0,0), (0,1,0), (0, $\frac{1}{\sqrt{2}}$, $-\frac{1}{\sqrt{2}}$)
(3) (1,0,0), (0, -1, 1), (0, 1, 1)
(4) None of the given answers is true.
