Question

Evaluate \(\begin{vmatrix}5&-4\\1&\sqrt{3}\end{vmatrix}\).

(a) 4\(\sqrt{3}\)+4

(b) 4\(\sqrt{3}\)+5

(c) 5\(\sqrt{3}\)+4

(d) 5\(\sqrt{3}\)-4

This question was posed to me in unit test.

Enquiry is from Determinant in portion Determinants of Mathematics – Class 12

Answer 1

The correct answer is (c) 5\(\sqrt{3}\)+4

Easiest explanation: Evaluating along R1, we get

∆=5(\(\sqrt{3}\))-(-4)1=5\(\sqrt{3}\)+4.