If \( A = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \), what is the determinant of A?
Practice Questions
1 question
Q1
If \( A = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \), what is the determinant of A?
ad - bc
bc - ad
a + d
b + c
The determinant of matrix A is given by the formula \( ad - bc \).
Questions & Step-by-step Solutions
1 item
Q
Q: If \( A = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \), what is the determinant of A?
Solution: The determinant of matrix A is given by the formula \( ad - bc \).
Steps: 3
Step 1: Identify the elements of the matrix A. The matrix A is given as A = [[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 is: determinant = (first element * second element of the second row) - (second element * first element of the second row). In our case, this translates to: determinant = (a * d) - (b * c).
Step 3: Write the final expression for the determinant. So, the determinant of matrix A is ad - bc.
