Question

Find the rank of the matrix $\left[\begin{array}{ccc}1&0&-4\\2&-1&3\end{array}\right]$

Answer 1

Answer:

Rank is 2.

Step-by-step explanation:

To find the rank of the given matrix  

$\left[\begin{array}{ccc}1&0&-4\\2&-1&3\end{array}\right]$

try to eliminate $A_{21}$ element by elemantary row operation

$R_{2} \:->\:R_{2}-2R_{1}\\\\ \left[\begin{array}{ccc}1&0&-4\\0&-1&11\end{array}\right]$

if we want to reduce it further,or try to reduce $A_{22}$ to zero.

but it cannot be.

so rank of the given matrix is two,as number of linearly independent rows are two.