What is the determinant of the matrix \( J = \begin{pmatrix} 5 & 6 \\ 7 &
Practice Questions
Q1
What is the determinant of the matrix \( J = \begin{pmatrix} 5 & 6 \\ 7 & 8 \end{pmatrix} \)? (2021)
-2
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Questions & Step-by-Step Solutions
What is the determinant of the matrix \( J = \begin{pmatrix} 5 & 6 \\ 7 & 8 \end{pmatrix} \)? (2021)
Step 1: Identify the elements of the matrix J. The matrix J is given as J = [[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 in the following arrangement: [[a, b], [c, d]].
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 determinant formula. Det(J) = (5 * 8) - (6 * 7).
Step 5: Calculate the first part of the formula: 5 * 8 = 40.
Step 6: Calculate the second part of the formula: 6 * 7 = 42.
Step 7: Subtract the second part from the first part: 40 - 42 = -2.
Step 8: Conclude that the determinant of the matrix J is -2.
