Question

5 For what value of b, the rank of the matrix is 2​

Answer 1

Answer:

1

Step-by-step explanation:

b =1

i think this is the ans.

Answer 2

Value of b is $-\frac{4}{7}$ .

Step 1: Find the value of b.

Given -  $A = \left[\begin{array}{ccc}1&5&4\\0&3&2\\b&13&10\end{array}\right]$

Rank of matrix = 2

∴If a $n$×$n$ matrix has a rank less than $n$, then the determinant is 0.

So, here determinant will also be 0.

So,    $|A| = \left|\begin{array}{ccc}1&5&4\\0&3&2\\b&13&10\end{array}\right|$

$|A| = 1(30-26)-5(0-2b)+4(0-3b)$

    = $4+10b-3b$

    = $4+7b$

As determinant must equal to 0 so,

$4+7b=0$

$b=-\frac{4}{7}$