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

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

Options:

Correct Answer: 10

Solution:

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

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

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

Step 1: Identify the elements of the matrix I. The matrix is I = [[3, 2], [1, 4]].
Step 2: Recognize the formula for the determinant of a 2x2 matrix, which is given by the formula: det(A) = ad - bc, where A = [[a, b], [c, d]].
Step 3: Assign the values from the matrix to the variables: a = 3, b = 2, c = 1, d = 4.
Step 4: Substitute the values into the determinant formula: det(I) = (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 I is 10.

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