Calculate the determinant \( \begin{vmatrix} 2 & 3 \\ 5 & 7 \end{vmatrix} \)

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Q: Calculate the determinant \( \begin{vmatrix} 2 & 3 \\ 5 & 7 \end{vmatrix} \)

Solution: The determinant is \( 2*7 - 3*5 = 14 - 15 = -1 \).

Steps: 8

Step 1: Identify the elements of the 2x2 matrix. The matrix is: [[2, 3], [5, 7]].
Step 2: Write down the formula for the determinant of a 2x2 matrix: det(A) = ad - bc, where A = [[a, b], [c, d]].
Step 3: Assign the values from the matrix to the variables: a = 2, b = 3, c = 5, d = 7.
Step 4: Substitute the values into the formula: det(A) = (2 * 7) - (3 * 5).
Step 5: Calculate the first part: 2 * 7 = 14.
Step 6: Calculate the second part: 3 * 5 = 15.
Step 7: Subtract the second part from the first part: 14 - 15 = -1.
Step 8: The determinant of the matrix is -1.