GATE CH 2022 | Question: 2

Question

Given matrix $A = \begin{bmatrix} x & 1 & 3\\ y & 2 & 6\\ 3 & 5 & 7 \end{bmatrix}$, the ordered pair $(x, y)$ for which $\text{det}(A) = 0 $ is

• A. $(1, 1)$
• B. $(1, 2)$
• C. $(2, 2)$
• D. $(2, 1)$

Answer 1

we know that if atleast one row or col is linear combination other row/col then the det is 0

if we take option (1,2) then the first and second row becomes same so det(A) = 0