Find the determinant of the matrix \( E = \begin{pmatrix} 3 & 2 \\ 1 & 4

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Question: Find the determinant of the matrix \\( E = \\begin{pmatrix} 3 & 2 \\\\ 1 & 4 \\end{pmatrix} \\). (2021)

Options:

Correct Answer: 10

Solution:

The determinant is \\( 3*4 - 2*1 = 12 - 2 = 10 \\).

Find the determinant of the matrix \( E = \begin{pmatrix} 3 & 2 \\ 1 & 4 \end{pmatrix} \). (2021)

Find the determinant of the matrix \( E = \begin{pmatrix} 3 & 2 \\ 1 & 4 \end{pmatrix} \). (2021)

Step 1: Identify the elements of the matrix E. The matrix is E = [[3, 2], [1, 4]].
Step 2: Write down the formula for the determinant of a 2x2 matrix. The formula is det(E) = (a * d) - (b * c), where a, b, c, and d are the elements of the matrix.
Step 3: Assign the values from the matrix to the variables in the formula. Here, a = 3, b = 2, c = 1, and d = 4.
Step 4: Substitute the values into the formula: det(E) = (3 * 4) - (2 * 1).
Step 5: Calculate the first part: 3 * 4 = 12.
Step 6: Calculate the second part: 2 * 1 = 2.
Step 7: Subtract the second part from the first part: 12 - 2 = 10.
Step 8: Conclude that the determinant of the matrix E is 10.

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