Compute the determinant of the 2×2 matrix \begin{bmatrix}13 & 7\\ 5 & 9\end{bmatrix}.

Compute the determinant of the $2 \times 2$ matrix \begin{bmatrix}13 & 7\\ 5 & 9\end{bmatrix}.

easy 1 mark Class 12 · Mathematics · Determinants

Answer

82

The correct answer is $82$ — Thus the determinant equals $82$ .

Identify the formula for a $2 \times 2$ determinant: $det [a c b d] = a d - b c$ .
Substitute $a = 13$ , $b = 7$ , $c = 5$ , $d = 9$ into the formula.
Compute the product of the main diagonal: $13 \times 9 = 117$ .
Compute the product of the off diagonal: $7 \times 5 = 35$ .
Subtract the off‑diagonal product from the main‑diagonal product: $117 - 35 = 82$ .
Thus the determinant equals $82$ .

Common mistake: Adding the two products instead of subtracting the off‑diagonal product.

Concept tested: Determinant of a $2\times2$ matrix