Q29Multiple correct3 Marks3 Dec 2023

Let $A$ be an $n\times n$ orthogonal matrix. Which statements are true?

A

The rows of $A$ form an orthonormal basis for $\mathbb{R}^n$.

B

Suppose $T$ is the linear transformation corresponding to $A$, then $\lVert Tv\rVert=\lVert v\rVert$ for any $v\in\mathbb{R}^n$.

C

The system $Ax=b$ has a unique solution for every $b\in\mathbb{R}^n$.

D

The rows of $A$ form an orthogonal basis but not an orthonormal basis for $\mathbb{R}^n$.