What is the value of the determinant \( \begin{vmatrix} a & b \\ c & d \end{vmatrix} \) when \( a = 1, b = 2, c = 3, d = 4 \)?

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Q: What is the value of the determinant \( \begin{vmatrix} a & b \\ c & d \end{vmatrix} \) when \( a = 1, b = 2, c = 3, d = 4 \)?

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

Steps: 7

Step 1: Identify the values of a, b, c, and d from the matrix. Here, a = 1, b = 2, c = 3, and d = 4.
Step 2: Write the formula for the determinant of a 2x2 matrix, which is given by the formula: determinant = a*d - b*c.
Step 3: Substitute the values into the formula: determinant = 1*4 - 2*3.
Step 4: Calculate 1*4, which equals 4.
Step 5: Calculate 2*3, which equals 6.
Step 6: Subtract the second result from the first: 4 - 6.
Step 7: The result of the subtraction is -2, which is the value of the determinant.