What is the value of the determinant of the matrix B = [[5, 1], [2, 3]]? (2022)

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Question: What is the value of the determinant of the matrix B = [[5, 1], [2, 3]]? (2022)

Options:

Correct Answer: 10

Exam Year: 2022

Solution:

Determinant of B = (5*3) - (1*2) = 15 - 2 = 13.

What is the value of the determinant of the matrix B = [[5, 1], [2, 3]]? (2022)

What is the value of the determinant of the matrix B = [[5, 1], [2, 3]]? (2022)

Step 1: Identify the elements of the matrix B. The matrix B is [[5, 1], [2, 3]]. This means: a = 5, b = 1, c = 2, d = 3.
Step 2: Use the formula for the determinant of a 2x2 matrix, which is: Det(B) = (a * d) - (b * c).
Step 3: Substitute the values into the formula: Det(B) = (5 * 3) - (1 * 2).
Step 4: Calculate the first part: 5 * 3 = 15.
Step 5: Calculate the second part: 1 * 2 = 2.
Step 6: Subtract the second part from the first part: 15 - 2 = 13.
Step 7: The value of the determinant of matrix B is 13.

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