If B = [[2, 3], [5, 7]], what is the value of det(B)? (2020)

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Question: If B = [[2, 3], [5, 7]], what is the value of det(B)? (2020)

Options:

Correct Answer: -1

Exam Year: 2020

Solution:

The determinant of B is calculated as (2*7) - (3*5) = 14 - 15 = -1.

If B = [[2, 3], [5, 7]], what is the value of det(B)? (2020)

If B = [[2, 3], [5, 7]], what is the value of det(B)? (2020)

Step 1: Identify the matrix B, which is [[2, 3], [5, 7]].
Step 2: Write down the formula for the determinant of a 2x2 matrix, which is det(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 = 2, b = 3, c = 5, d = 7.
Step 4: Substitute the values into the determinant formula: det(B) = (2*7) - (3*5).
Step 5: Calculate the first part: 2*7 = 14.
Step 6: Calculate the second part: 3*5 = 15.
Step 7: Subtract the second part from the first part: 14 - 15 = -1.
Step 8: Conclude that the value of det(B) is -1.

Determinant of a 2x2 Matrix – The determinant of a 2x2 matrix B = [[a, b], [c, d]] is calculated using the formula det(B) = ad - bc.