Question

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

Answer 1

Answer:

Rank of matrix:3

Step-by-step explanation:

to find the rank of the matrix try to eliminate$A_{21},A_{31}$ elements by elemantary row operation

$R_{2}=> R_{2}-2R_{1}\\\\  \left[\begin{array}{ccc}1&4&-1\\0&-5&2\\0&1&2\end{array}\right] \\\\\\R_{3}=> R_{3}+\frac{1}{5} R_{2}\\\\ \left[\begin{array}{ccc}1&4&-1\\0&-5&2\\0&0&\frac{12}{5} \end{array}\right]$

here it cannot be reduced further.

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