Question

Find the rank of the matrix $\left[\begin{array}{ccc}1&1&1\\1&1&1\\1&1&1\end{array}\right]$

Answer 1

Answer:

Rank of matrix:1

Step-by-step explanation:

To find the rank of the matrix,try to reduced$A_{21} ,A_{31}$ to zero.

$\left[\begin{array}{ccc}1&1&1\\1&1&1\\1&1&1\end{array}\right] \\\\R_{3} =>R_{3}-R_{1}\\\\ \left[\begin{array}{ccc}1&1&1\\1&1&1\\0&0&0\end{array}\right] \\\\R_{2} =>R_{2}-R_{1}\\\\\left[\begin{array}{ccc}1&1&1\\0&0&0\\0&0&0\end{array}\right]$

So,rank of the given matrix is one,as number of linearly independent row is one here.