Q29Multiple correct4 Marks5 Jun 2022

Choose the set of correct options.

A

If $v$ and $w$ are linearly independent, then $v+w$ and $w$ are also linearly independent.

B

If $A^n=0$ for some $2\times2$ matrix $A$ and some non-zero natural number $n$, then $A$ must be the zero matrix of order $2$.

C

If a homogeneous system of linear equations $Ax=0$ has a non-zero solution, then it must have infinitely many solutions.

D

If $A^3=I$ for some $n\times n$ matrix $A$, then it is not necessary that $A^2$ is an invertible matrix.