If \( B = \begin{pmatrix} 1 & 2 \\ 3 & 5 \end{pmatrix} \), what is \( |B

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Question: If \\( B = \\begin{pmatrix} 1 & 2 \\\\ 3 & 5 \\end{pmatrix} \\), what is \\( |B| \\)?

Options:

Correct Answer: 1

Solution:

The determinant is \\( 1*5 - 2*3 = 5 - 6 = -1 \\).

If \( B = \begin{pmatrix} 1 & 2 \\ 3 & 5 \end{pmatrix} \), what is \( |B| \)?

If \( B = \begin{pmatrix} 1 & 2 \\ 3 & 5 \end{pmatrix} \), what is \( |B| \)?

Step 1: Identify the matrix B, which is given as B = [[1, 2], [3, 5]].
Step 2: Recall the formula for the determinant of a 2x2 matrix, which is |B| = (a*d) - (b*c), where the matrix is [[a, b], [c, d]].
Step 3: Assign the values from matrix B to the variables: a = 1, b = 2, c = 3, d = 5.
Step 4: Substitute the values into the determinant formula: |B| = (1*5) - (2*3).
Step 5: Calculate the first part: 1*5 = 5.
Step 6: Calculate the second part: 2*3 = 6.
Step 7: Subtract the second part from the first part: 5 - 6 = -1.
Step 8: Conclude that the determinant |B| is -1.

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