Find the determinant of E = [[3, 2], [1, 4]]. (2022)

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Question: Find the determinant of E = [[3, 2], [1, 4]]. (2022)

Options:

Correct Answer: 10

Exam Year: 2022

Solution:

Det(E) = (3*4) - (2*1) = 12 - 2 = 10.

Find the determinant of E = [[3, 2], [1, 4]]. (2022)

Find the determinant of E = [[3, 2], [1, 4]]. (2022)

Step 1: Identify the elements of the matrix E = [[3, 2], [1, 4]]. The elements are: a = 3, b = 2, c = 1, d = 4.
Step 2: Use the formula for the determinant of a 2x2 matrix, which is Det(E) = (a * d) - (b * c).
Step 3: Substitute the values into the formula: Det(E) = (3 * 4) - (2 * 1).
Step 4: Calculate the first part: 3 * 4 = 12.
Step 5: Calculate the second part: 2 * 1 = 2.
Step 6: Subtract the second part from the first part: 12 - 2 = 10.
Step 7: The determinant of the matrix E is 10.

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