What is the determinant of the matrix \( C = \begin{pmatrix} 5 & 6 \\ 7 &
Practice Questions
Q1
What is the determinant of the matrix \( C = \begin{pmatrix} 5 & 6 \\ 7 & 8 \end{pmatrix} \)? (2020)
-2
2
0
1
Questions & Step-by-Step Solutions
What is the determinant of the matrix \( C = \begin{pmatrix} 5 & 6 \\ 7 & 8 \end{pmatrix} \)? (2020)
Step 1: Identify the elements of the matrix C. The matrix is C = [[5, 6], [7, 8]].
Step 2: Write down the formula for the determinant of a 2x2 matrix. The formula is: det(C) = (a * d) - (b * c), where a, b, c, and d are the elements of the matrix.
Step 3: Assign the values from the matrix to the variables in the formula. Here, a = 5, b = 6, c = 7, d = 8.
Step 4: Substitute the values into the formula: det(C) = (5 * 8) - (6 * 7).
Step 5: Calculate 5 * 8, which equals 40.
Step 6: Calculate 6 * 7, which equals 42.
Step 7: Subtract the second result from the first: 40 - 42.
Step 8: The result is -2, so the determinant of the matrix C is -2.
