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Calculate the determinant of \( D = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{
Calculate the determinant of \( D = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix} \). (2021)
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Calculate the determinant of \( D = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix} \). (2021)
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The determinant is \( 0*0 - 1*1 = 0 - 1 = -1 \).
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Q
Q: Calculate the determinant of \( D = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix} \). (2021)
Solution:
The determinant is \( 0*0 - 1*1 = 0 - 1 = -1 \).
Steps: 8
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Step 1: Identify the matrix D, which is D = [[0, 1], [1, 0]].
Step 2: Recall the formula for the determinant of a 2x2 matrix, which is given by det(A) = ad - bc, where A = [[a, b], [c, d]].
Step 3: Assign the values from the matrix D to the variables: a = 0, b = 1, c = 1, d = 0.
Step 4: Substitute the values into the determinant formula: det(D) = (0 * 0) - (1 * 1).
Step 5: Calculate the first part: 0 * 0 = 0.
Step 6: Calculate the second part: 1 * 1 = 1.
Step 7: Subtract the second part from the first part: 0 - 1 = -1.
Step 8: Conclude that the determinant of matrix D is -1.
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