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

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Question: Calculate the determinant of the matrix \\( G = \\begin{pmatrix} 2 & 1 \\\\ 3 & 4 \\end{pmatrix} \\). (2020)

Options:

Correct Answer: 5

Exam Year: 2020

Solution:

The determinant is \\( 2*4 - 1*3 = 8 - 3 = 5 \\).

Calculate the determinant of the matrix \( G = \begin{pmatrix} 2 & 1 \\ 3 & 4 \end{pmatrix} \). (2020)

Calculate the determinant of the matrix \( G = \begin{pmatrix} 2 & 1 \\ 3 & 4 \end{pmatrix} \). (2020)

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

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