Questions: Find the determinant of matrix A=[3 -2; 5 3]

Transcript text: Find the determinant of matrix $A=\left[\begin{array}{cc}3 & -2 \\ 5 & 3\end{array}\right]$

Solution

Solution Steps

Step 1: Define the Matrix

Given the matrix $ A = \begin{bmatrix} 3 & -2 \\ 5 & 3 \end{bmatrix} $.

Step 2: Apply the Determinant Formula

For a $ 2 \times 2 $ matrix $ A = \begin{bmatrix} a & b \\ c & d \end{bmatrix} $, the determinant is calculated as: \[ \text{det}(A) = ad - bc \] Substituting the values from matrix $ A $: \[ a = 3, \quad b = -2, \quad c = 5, \quad d = 3 \] \[ \text{det}(A) = (3 \cdot 3) - (-2 \cdot 5) \]

Step 3: Perform the Calculations

\[ \text{det}(A) = 9 - (-10) = 9 + 10 = 19 \]