Determinants
General
Grade 12
Question:
Find the value of $\begin{vmatrix} 1 & 2 \\ -1 & 3 \end{vmatrix} \times \begin{vmatrix} 3 & 0 \\ -1 & 4 \end{vmatrix}$ and prove that it is equal to $\begin{vmatrix} 1 & 8 \\ -6 & 12 \end{vmatrix}$.
Step-by-Step Solution
Key Concept: General
$\begin{vmatrix} 1 & 2 \\ -1 & 3 \end{vmatrix} \times \begin{vmatrix} 3 & 0 \\ -1 & 4 \end{vmatrix} = \begin{vmatrix} 1 \times 3 - 2 \times 1 & 1 \times 0 + 2 \times 4 \\ -1 \times 3 + 3 \times (-1) & -1 \times 0 + 3 \times 4 \end{vmatrix} = \begin{vmatrix} 1 & 8 \\ -6 & 12 \end{vmatrix} = 60$
Correct Answer: A