Find the determinant of the matrix \( \begin{pmatrix} 2 & 1 \\ 3 & 4 \end{pmatrix} \).
Practice Questions
1 question
Q1
Find the determinant of the matrix \( \begin{pmatrix} 2 & 1 \\ 3 & 4 \end{pmatrix} \).
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The determinant is calculated as \( 2*4 - 1*3 = 8 - 3 = 5 \).
Questions & Step-by-step Solutions
1 item
Q
Q: Find the determinant of the matrix \( \begin{pmatrix} 2 & 1 \\ 3 & 4 \end{pmatrix} \).
Solution: The determinant is calculated as \( 2*4 - 1*3 = 8 - 3 = 5 \).
Steps: 6
Step 1: Identify the elements of the matrix. The matrix is \( \begin{pmatrix} 2 & 1 \\ 3 & 4 \end{pmatrix} \). The elements are: a = 2, b = 1, c = 3, d = 4.
Step 2: Use the formula for the determinant of a 2x2 matrix, which is given by \( ad - bc \).
Step 3: Substitute the values into the formula. Here, a = 2, b = 1, c = 3, d = 4. So, we calculate: \( 2*4 - 1*3 \).
Step 4: Perform the multiplication: \( 2*4 = 8 \) and \( 1*3 = 3 \).
Step 5: Subtract the second result from the first: \( 8 - 3 = 5 \).
