What is the determinant of the matrix \( \begin{pmatrix} 3 & 2 \\ 1 & 4 \end{pmatrix} \)?
Practice Questions
1 question
Q1
What is the determinant of the matrix \( \begin{pmatrix} 3 & 2 \\ 1 & 4 \end{pmatrix} \)?
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The determinant is calculated as (3*4) - (2*1) = 12 - 2 = 10.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the determinant of the matrix \( \begin{pmatrix} 3 & 2 \\ 1 & 4 \end{pmatrix} \)?
Solution: The determinant is calculated as (3*4) - (2*1) = 12 - 2 = 10.
Steps: 7
Step 1: Identify the elements of the matrix. The matrix is: \( \begin{pmatrix} 3 & 2 \\ 1 & 4 \end{pmatrix} \). The elements are: a = 3, b = 2, c = 1, d = 4.
Step 2: Use the formula for the determinant of a 2x2 matrix, which is: \( \text{det} = (a \cdot d) - (b \cdot c) \).
Step 3: Substitute the values into the formula: \( \text{det} = (3 \cdot 4) - (2 \cdot 1) \).
Step 4: Calculate the first part: \( 3 \cdot 4 = 12 \).
Step 5: Calculate the second part: \( 2 \cdot 1 = 2 \).
Step 6: Subtract the second part from the first part: \( 12 - 2 = 10 \).
