What is the value of \( \begin{vmatrix} 2 & 1 \\ 3 & 4 \end{vmatrix} \)?

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Question: What is the value of \\( \\begin{vmatrix} 2 & 1 \\\\ 3 & 4 \\end{vmatrix} \\)? (2022)

Options:

Correct Answer: 5

Exam Year: 2022

Solution:

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

What is the value of \( \begin{vmatrix} 2 & 1 \\ 3 & 4 \end{vmatrix} \)? (2022)

What is the value of \( \begin{vmatrix} 2 & 1 \\ 3 & 4 \end{vmatrix} \)? (2022)

Step 1: Identify the elements of the 2x2 matrix. The matrix is: [[2, 1], [3, 4]].
Step 2: Write down the formula for the determinant of a 2x2 matrix, which is: det(A) = (a * d) - (b * c), where A = [[a, b], [c, d]].
Step 3: Assign the values from the matrix to the variables: a = 2, b = 1, c = 3, d = 4.
Step 4: Substitute the values into the determinant formula: det(A) = (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 value of the determinant is 5.

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