For the matrix E = [[1, 2], [2, 4]], what is the determinant? (2021)

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Question: For the matrix E = [[1, 2], [2, 4]], what is the determinant? (2021)

Options:

Correct Answer: 0

Solution:

Determinant of E = (1*4) - (2*2) = 4 - 4 = 0.

For the matrix E = [[1, 2], [2, 4]], what is the determinant? (2021)

For the matrix E = [[1, 2], [2, 4]], what is the determinant? (2021)

Step 1: Identify the elements of the matrix E. The matrix E is [[1, 2], [2, 4]].
Step 2: Label the elements of the matrix. Let a = 1, b = 2, c = 2, d = 4.
Step 3: Use the formula for the determinant of a 2x2 matrix, which is: determinant = (a * d) - (b * c).
Step 4: Substitute the values into the formula: determinant = (1 * 4) - (2 * 2).
Step 5: Calculate the first part: 1 * 4 = 4.
Step 6: Calculate the second part: 2 * 2 = 4.
Step 7: Subtract the second part from the first part: 4 - 4 = 0.
Step 8: Conclude that the determinant of the matrix E is 0.

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