Question

Evaluate \(\begin{vmatrix}x^2&x^3&x^4\\x&y&z\\x^2&x^3&x^4 \end{vmatrix}\).

(a) 0

(b) 1

(c) xyz

(d) x^2 yz^3

I had been asked this question in my homework.

This interesting question is from Properties of Determinants in chapter Determinants of Mathematics – Class 12

Answer 1

The correct answer is (a) 0

The best I can explain: Δ=\(\begin{vmatrix}x^2&x^3&x^4\\x&y&z\\x^2&x^3&x^4 \end{vmatrix}\)

If the elements of any two rows or columns are identical, then the value of determinant is zero. Here, the elements of row 1 and row 3 are identical. Hence, its determinant is 0.