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

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Question: If \\( B = \\begin{pmatrix} 2 & 3 \\\\ 1 & 4 \\end{pmatrix} \\), what is \\( |B| \\)? (2022)

Options:

Correct Answer: 5

Solution:

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

If \( B = \begin{pmatrix} 2 & 3 \\ 1 & 4 \end{pmatrix} \), what is \( |B| \)? (2022)

If \( B = \begin{pmatrix} 2 & 3 \\ 1 & 4 \end{pmatrix} \), what is \( |B| \)? (2022)

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 of matrix B is |B| = 5.

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