What is the value of \( |D| \) for the matrix \( D = \begin{pmatrix} 0 & 1 \

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Question: What is the value of \\( |D| \\) for the matrix \\( D = \\begin{pmatrix} 0 & 1 \\\\ 1 & 0 \\end{pmatrix} \\)? (2023)

Options:

Correct Answer: 1

Solution:

The determinant is \\( 0*0 - 1*1 = 0 - 1 = -1 \\).

What is the value of \( |D| \) for the matrix \( D = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix} \)? (2023)

What is the value of \( |D| \) for the matrix \( D = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix} \)? (2023)

Step 1: Identify the matrix D, which is D = [[0, 1], [1, 0]].
Step 2: Write down the formula for the determinant of a 2x2 matrix, which is |D| = a*d - b*c, where the matrix is [[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: |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 value of |D| is -1.

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