Question

If the matrix $A=\left[\begin{array}{cccc}1& 2& 3& 0\\ 2& 4& 3& 2\\ 3& 2& 1& 3\\ 6& 8& 7& \alpha \end{array}\right]$ is of rank 3, then $\alpha =$

• A. $1$
• B. $5$
• C. $4$
• D. $-4$

Answer 1

The correct option is B $5$

Since the matrix has $3$ linear independent rows.

then $R_4$ must be linear combination of $R_1,R_2,R_3$
$R_4=R_1+R_2+R_3$

$\therefore \alpha =0+2+3$
$\therefore \alpha =5$