Question

question 1-3
find the determinant of matrix a.
$a = \

$$\begin{bmatrix} 2 & 4 \\\\ -3 & 1 \\end{bmatrix}$$

$
\\(\circ\\) 14
\\(\circ\\) 3
\\(\circ\\) -14
\\(\circ\\) 0
\\(\circ\\) 10

Explanation:

Step1: Recall determinant formula for 2x2 matrix

For a matrix \(

$$\begin{bmatrix} a & b \\ c & d \end{bmatrix}$$

\), the determinant is \( ad - bc \).

Step2: Identify matrix elements

In matrix \( A =

$$\begin{bmatrix} 2 & 4 \\ -3 & 1 \end{bmatrix}$$

\), \( a = 2 \), \( b = 4 \), \( c = -3 \), \( d = 1 \).

Step3: Calculate determinant

Substitute into the formula: \( (2)(1) - (4)(-3) = 2 + 12 = 14 \). Wait, no, wait: Wait, \( (2)(1) - (4)(-3) = 2 + 12 = 14 \)? Wait, no, wait, let's recalculate. Wait, \( ad - bc = (2)(1) - (4)(-3) = 2 + 12 = 14 \)? Wait, but wait, the options have 14 as an option. Wait, but let me check again. Wait, \( 2*1 = 2 \), \( 4*(-3) = -12 \), so \( 2 - (-12) = 2 + 12 = 14 \). Yes.

Answer:

14 (corresponding to the option with text "14")