Calculate the determinant of the matrix \( \begin{pmatrix} 2 & 3 \\ 5 &
Practice Questions
Q1
Calculate the determinant of the matrix \( \begin{pmatrix} 2 & 3 \\ 5 & 7 \end{pmatrix} \).
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Questions & Step-by-Step Solutions
Calculate the determinant of the matrix \( \begin{pmatrix} 2 & 3 \\ 5 & 7 \end{pmatrix} \).
Correct Answer: -1
Step 1: Identify the elements of the matrix. The matrix is \( \begin{pmatrix} 2 & 3 \\ 5 & 7 \end{pmatrix} \). The elements are: a = 2, b = 3, c = 5, d = 7.
Step 2: Use the formula for the determinant of a 2x2 matrix, which is given by: \( \text{det} = (a \cdot d) - (b \cdot c) \).
Step 3: Substitute the values into the formula: \( \text{det} = (2 \cdot 7) - (3 \cdot 5) \).
Step 4: Calculate the first part: \( 2 \cdot 7 = 14 \).
Step 5: Calculate the second part: \( 3 \cdot 5 = 15 \).
Step 6: Subtract the second part from the first part: \( 14 - 15 = -1 \).
Step 7: The determinant of the matrix is \( -1 \).
