Question

The rank of the matrix (m × n) where m<n cannot be more than?

(a) m

(b) n

(c) m*n

(d) m-n

I got this question in an online quiz.

My question is based upon Basics of Linear Algebra topic in chapter Linear Algebra Overview of Signals and Systems

Answer 1

Right option is (a) m

Explanation: let us consider a 2×3 matrix \(\begin{bmatrix}

1 & 1 & 1\\

4 & 5 & 6\\

\end{bmatrix}\)

Where R1≠R2  rank is 2

Another 2×3  matrix \(\begin{bmatrix}

1 & 1 & 1\\

1 & 1 & 1\\

\end{bmatrix}\)

Here, R1=R2 rank is 1

And the rank of these two matrices is 1, 2

So rank is cannot be more than m.