If \( A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \), find \( |A| \

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Question: If \\( A = \\begin{pmatrix} 1 & 2 \\\\ 3 & 4 \\end{pmatrix} \\), find \\( |A| \\).

Options:

Correct Answer: -2

Solution:

The determinant is \\( 1*4 - 2*3 = 4 - 6 = -2 \\).

If \( A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \), find \( |A| \).

If \( A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \), find \( |A| \).

Correct Answer: -2

Step 1: Identify the elements of the matrix A. The matrix A is given as A = [[1, 2], [3, 4]].
Step 2: Write down the formula for the determinant of a 2x2 matrix. The formula is |A| = (a * d) - (b * c), where the matrix is [[a, b], [c, d]].
Step 3: Assign the values from the matrix to the variables in the formula. Here, a = 1, b = 2, c = 3, and d = 4.
Step 4: Substitute the values into the determinant formula. This gives us |A| = (1 * 4) - (2 * 3).
Step 5: Calculate the products. First, calculate 1 * 4 = 4. Then, calculate 2 * 3 = 6.
Step 6: Subtract the second product from the first. So, 4 - 6 = -2.
Step 7: Write down the final result. The determinant |A| is -2.

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