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

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

Solution: The determinant is \( 1*4 - 2*3 = 4 - 6 = -2 \).

Steps: 8

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