Q18Multiple correct4 Marks28 Apr 2024

Choose the correct option(s) from the following:

A

The orthonormal set obtained from {(0,1), (-1,3)} using Gram-Schmidt process is {(0,1), (-1,0)}.

B

$\begin{bmatrix} 1 & -2 \\ 2 & 1 \end{bmatrix}$ is an orthogonal matrix.

C

Let W = {(x,y,z) in $\mathbb{R}^3$ : x + 2y + z = 0}. If u = $(1, -1, 1)$ and if P_W is the projection from $\mathbb{R}^3$ to W, then P_W(u) = u.

D

The determinant of a matrix formed by 3 orthonormal vectors in $\mathbb{R}^3$ is always 1.