What is the determinant of the matrix \( F = \begin{pmatrix} 2 & 5 \\ 3 &
Practice Questions
Q1
What is the determinant of the matrix \( F = \begin{pmatrix} 2 & 5 \\ 3 & 7 \end{pmatrix} \)? (2023)
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Questions & Step-by-Step Solutions
What is the determinant of the matrix \( F = \begin{pmatrix} 2 & 5 \\ 3 & 7 \end{pmatrix} \)? (2023)
Step 1: Identify the elements of the matrix F. The matrix is F = (2, 5; 3, 7). This means the first row has 2 and 5, and the second row has 3 and 7.
Step 2: Use the formula for the determinant of a 2x2 matrix, which is det(F) = (first element * second element of the second row) - (second element * first element of the second row).
Step 3: Substitute the values into the formula: det(F) = (2 * 7) - (5 * 3).
Step 4: Calculate the first part: 2 * 7 = 14.
Step 5: Calculate the second part: 5 * 3 = 15.
Step 6: Subtract the second part from the first part: 14 - 15 = -1.
