Rank of Matrices

Algebra Level 2

[ 1 3 2 2 1 2 1 3 2 4 3 4 3 7 4 8 ] \quad \begin{bmatrix} 1\quad & 3\quad & 2\quad & 2 \\ 1\quad & 2\quad & 1\quad & 3 \\ 2\quad & 4\quad & 3\quad & 4 \\ 3\quad & 7\quad & 4\quad & 8 \end{bmatrix}

Find the rank of the matrix above.


The answer is 3.

Swapnil Roge by Swapnil Roge , 23, India

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1 solution

Tom Engelsman
Sep 15, 2020

After performing elementary row operations to find the reduced-row echleon form:

[ 1 0 0 3 0 1 0 1 0 0 1 − 2 0 0 0 0 ] \begin{bmatrix} 1 & 0 & 0 & 3 \\ 0 & 1 & 0 & 1 \\ 0 & 0 & 1 & -2 \\ 0 & 0 & 0 & 0 \end{bmatrix}

we have three linearly-independent columns ⇒ \Rightarrow the rank equals 3 . \boxed{3}.

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