Calculate the determinant of the matrix \( C = \begin{pmatrix} 5 & 6 \\ 7 & 8 \end{pmatrix} \). (2020)
Practice Questions
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Q1
Calculate the determinant of the matrix \( C = \begin{pmatrix} 5 & 6 \\ 7 & 8 \end{pmatrix} \). (2020)
-2
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0
1
The determinant is \( 5*8 - 6*7 = 40 - 42 = -2 \).
Questions & Step-by-step Solutions
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Q
Q: Calculate the determinant of the matrix \( C = \begin{pmatrix} 5 & 6 \\ 7 & 8 \end{pmatrix} \). (2020)
Solution: The determinant is \( 5*8 - 6*7 = 40 - 42 = -2 \).
Steps: 8
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, and d = 8.
Step 4: Substitute the values into the formula: det(C) = (5 * 8) - (6 * 7).
Step 5: Calculate the first part: 5 * 8 = 40.
Step 6: Calculate the second part: 6 * 7 = 42.
Step 7: Subtract the second part from the first part: 40 - 42 = -2.
Step 8: Write down the final result: The determinant of the matrix C is -2.
