Question

Evaluate \(\begin{vmatrix}4&8&12\\6&12&18\\7&14&21\end{vmatrix}\).

(a) 168

(b) -1

(c) -168

(d) 0

This question was addressed to me in exam.

Query is from Properties of Determinants in division Determinants of Mathematics – Class 12

Answer 1

Right answer is (d) 0

Explanation: Δ=\(\begin{vmatrix}4&8&12\\6&12&18\\7&14&21\end{vmatrix}\)

Taking 4, 6 and 7 from R1, R2, R3 respectively

Δ=4×6×7\(\begin{vmatrix}1&2&3\\1&2&3\\1&2&3\end{vmatrix}\)

Since the elements of all rows are identical, the determinant is zero.