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

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Question: Calculate the determinant of the matrix \\( I = \\begin{pmatrix} 3 & 2 \\\\ 1 & 4 \\end{pmatrix} \\). (2023)

Options:

Correct Answer: 10

Exam Year: 2023

Solution:

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

Calculate the determinant of the matrix \( I = \begin{pmatrix} 3 & 2 \\ 1 & 4 \end{pmatrix} \). (2023)

Calculate the determinant of the matrix \( I = \begin{pmatrix} 3 & 2 \\ 1 & 4 \end{pmatrix} \). (2023)

Step 1: Identify the elements of the matrix I, which is given as I = [[3, 2], [1, 4]].
Step 2: Write down the formula for the determinant of a 2x2 matrix, which is Det(I) = (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: 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 product of a and d: 3*4 = 12.
Step 6: Calculate the product of b and c: 2*1 = 2.
Step 7: Subtract the second product from the first: 12 - 2 = 10.
Step 8: Conclude that the determinant of the matrix I is 10.

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