ISRO CSE 2023 | Question: 30

Question

Given $P$ is a matrix $=\left(\begin{array}{llll}3 & 2 & 1 & 4 \\ 4 & 0 & 3 & 1 \\ 6 & 4 & 2 & 8 \\ 2 & 5 & 1 & 3\end{array}\right)$

If $\operatorname{det}|\mathrm{P}|$ denotes the determinant of matrix $P$, then which of the following is true:

• A. $\operatorname{det}|\mathrm{P}|$ is indeterminate
• B. $\operatorname{det}|\mathrm{P}|$ is negative
• C. $\operatorname{det}|\mathrm{P}|=0$
• D. None of the above

   

Comments

Rows 1 and 3 are scalar multiples of each other..
So, the determinant of P will be 0.

Answer 1

ans (c):det |P| = 0
taking 2 as common from row 3 then row 1 and row 3 will become same so, acording to determinant property |P| = 0

Answer 2

Correct answer is option C and here is the explanation