Question

What is the value of k if \(\begin{vmatrix}y + z & x & x \\y & z + x & y \\z & z & x + y\end {vmatrix}\) ?

(a) 4

(b) -4

(c) 1

(d) 0

I had been asked this question in an interview for job.

Asked question is from Application of Determinants in portion Determinants of Mathematics – Class 12

Answer 1

Correct answer is (a) 4

Explanation: Put the value of x, y, z = 1

Thus, putting the value of x = 1, y = 1 and z = 1 on both sides, we get

\(\begin{vmatrix}2 & 1 & 1 \\1 & 2 & 1 \\1 & 1 & 2 \end {vmatrix}\) = k

So, solving the determinant we get k = 4.