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Find the value of the determinant \( \begin{pmatrix} a & b \\ c & d \end
Find the value of the determinant \( \begin{pmatrix} a & b \\ c & d \end{pmatrix} \) when \( a=1, b=2, c=3, d=4 \).
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Find the value of the determinant \( \begin{pmatrix} a & b \\ c & d \end{pmatrix} \) when \( a=1, b=2, c=3, d=4 \).
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The determinant is \( 1*4 - 2*3 = 4 - 6 = -2 \).
Questions & Step-by-step Solutions
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Q: Find the value of the determinant \( \begin{pmatrix} a & b \\ c & d \end{pmatrix} \) when \( a=1, b=2, c=3, d=4 \).
Solution:
The determinant is \( 1*4 - 2*3 = 4 - 6 = -2 \).
Steps: 7
Show Steps
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 \( -2 \).
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