Find the value of the determinant \( \begin{pmatrix} a & b \\ c & d \end

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Question: Find the value of the determinant \\( \\begin{pmatrix} a & b \\\\ c & d \\end{pmatrix} \\) when \\( a=1, b=2, c=3, d=4 \\).

Options:

Correct Answer: -2

Solution:

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

Find the value of the determinant \( \begin{pmatrix} a & b \\ c & d \end{pmatrix} \) when \( a=1, b=2, c=3, d=4 \).

Find the value of the determinant \( \begin{pmatrix} a & b \\ c & d \end{pmatrix} \) when \( a=1, b=2, c=3, d=4 \).

Step 1: Identify the elements of the matrix. The matrix is \( \begin{pmatrix} a & b \\ c & d \end{pmatrix} \) with values \( a=1, b=2, c=3, d=4 \).
Step 2: Write down the formula for the determinant of a 2x2 matrix. The formula is \( \text{det} = ad - bc \).
Step 3: Substitute the values into the formula. Here, \( a=1, b=2, c=3, d=4 \), so we have \( \text{det} = 1*4 - 2*3 \).
Step 4: Calculate the first part of the formula. Multiply \( 1*4 = 4 \).
Step 5: Calculate the second part of the formula. Multiply \( 2*3 = 6 \).
Step 6: Subtract the second part from the first part. So, \( 4 - 6 = -2 \).
Step 7: The value of the determinant is \( -2 \).

Determinant Calculation – The determinant of a 2x2 matrix is calculated using the formula ad - bc.