Systems of Linear Equations Previous Year Questions (PYQs) for CMI M.Sc. and Ph.D. Computer Science: 3+ Solved Questions with Step-by-Step Solutions

$A^{-1}$ does not exist.

The equation $A^{T}x=b$ also does not admit any solution.

$|A|=0$.

Suppose $c$ is another $n\times 1$ vector such that $Ax=c$ also does not admit a solution. Then the vector $c$ is a constant multiple of the vector $b$.

Rank of $A$ is 12.

Rank of $A$ and $B$ are not related.

If $v$ is a vector such that $Av=0$ then $Bv$ is also 0.

Rank of $B$ is at most 11.

If equation (1) admits a solution for all $b$, then $A^{-1}$ exists.

If equation (1) admits a solution for all $b$, then equation (2) also admits a solution for all $b$.

If equation (1) admits a solution for some $b$, then $A^{-1}$ exists.

If equation (1) admits a solution for some $b$, then equation (2) also admits a solution for that $b$.