If \( C = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \), what is the determinant of C?
Practice Questions
1 question
Q1
If \( C = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \), what is the determinant of C?
ad - bc
bc - ad
a + d
b + c
The determinant of C is given by the formula \( ad - bc \).
Questions & Step-by-step Solutions
1 item
Q
Q: If \( C = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \), what is the determinant of C?
Solution: The determinant of C is given by the formula \( ad - bc \).
Steps: 4
Step 1: Identify the elements of the matrix C. The matrix C is given as C = [[a, b], [c, d]]. This means a is in the first row and first column, b is in the first row and second column, c is in the second row and first column, and d is in the second row and second column.
Step 2: Use the formula for the determinant of a 2x2 matrix. The formula for the determinant of a matrix C = [[a, b], [c, d]] is given by the expression ad - bc.
Step 3: Apply the formula. To find the determinant, multiply a and d together to get ad, and multiply b and c together to get bc. Then subtract the second product (bc) from the first product (ad).
Step 4: Write the final result. The determinant of the matrix C is ad - bc.
