Q2Multiple correct8 Marks21 Dec 2025

Choose the set of correct options.

A

Any subset of a linearly independent set of vectors is linearly dependent.

B

Let A be an n x n matrix. If A is invertible, then adj(A)x = b has a solution.

C

Suppose A and B are two n x n matrices with the same row reduced echelon forms. Then A is similar to B.

D

In an inner product space (V, <.,.>), an orthogonal subset of non-zero vectors in V is also a linearly independent subset.

E

Consider $\mathbb{R}^3$ with the usual inner product. Let $T: \mathbb{R}^3 \to \mathbb{R}$^$3$ be a linear transformation defined by T(v) = Av where A is an orthogonal matrix. Then T may not be an orthogonal transformation.