Calculate the determinant of J = [[5, 6], [7, 8]]. (2014)
Practice Questions
1 question
Q1
Calculate the determinant of J = [[5, 6], [7, 8]]. (2014)
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Det(J) = (5*8) - (6*7) = 40 - 42 = -2.
Questions & Step-by-step Solutions
1 item
Q
Q: Calculate the determinant of J = [[5, 6], [7, 8]]. (2014)
Solution: Det(J) = (5*8) - (6*7) = 40 - 42 = -2.
Steps: 8
Step 1: Identify the elements of the matrix J. The matrix J is [[5, 6], [7, 8]].
Step 2: Write down the formula for the determinant of a 2x2 matrix. The formula is Det(J) = (a*d) - (b*c), where a, b, c, and d are the elements of the matrix [[a, b], [c, d]].
Step 3: Assign the values from the matrix to the variables: a = 5, b = 6, c = 7, d = 8.
Step 4: Substitute the values into the formula: Det(J) = (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.
