If \( B = \begin{pmatrix} 2 & 3 \\ 1 & 4 \end{pmatrix} \), find \( |B| \

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Question: If \\( B = \\begin{pmatrix} 2 & 3 \\\\ 1 & 4 \\end{pmatrix} \\), find \\( |B| \\).

Options:

Correct Answer: 5

Solution:

The determinant is \\( 2*4 - 3*1 = 8 - 3 = 5 \\).

If \( B = \begin{pmatrix} 2 & 3 \\ 1 & 4 \end{pmatrix} \), find \( |B| \).

If \( B = \begin{pmatrix} 2 & 3 \\ 1 & 4 \end{pmatrix} \), find \( |B| \).

Correct Answer: 5

Step 1: Identify the matrix B, which is given as B = [[2, 3], [1, 4]].
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 a, b, c, and d: a = 2, b = 3, c = 1, d = 4.
Step 4: Substitute the values into the determinant formula: |B| = (2*4) - (3*1).
Step 5: Calculate 2*4, which equals 8.
Step 6: Calculate 3*1, which equals 3.
Step 7: Subtract the second result from the first: 8 - 3 = 5.
Step 8: Conclude that the determinant |B| is 5.

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