If \( A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \), what is \( |A| \)?
Practice Questions
1 question
Q1
If \( A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \), what is \( |A| \)?
-2
2
0
4
The determinant is calculated as (1*4) - (2*3) = 4 - 6 = -2.
Questions & Step-by-step Solutions
1 item
Q
Q: If \( A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \), what is \( |A| \)?
Solution: The determinant is calculated as (1*4) - (2*3) = 4 - 6 = -2.
Steps: 7
Step 1: Identify the elements of the matrix A. The matrix A is given as A = [[1, 2], [3, 4]].
Step 2: Write down the formula for the determinant of a 2x2 matrix. The formula is |A| = (a*d) - (b*c), where a, b, c, and d are the elements of the matrix.
Step 3: Assign the values from the matrix to the variables in the formula. Here, a = 1, b = 2, c = 3, d = 4.
Step 4: Substitute the values into the formula. This gives us |A| = (1*4) - (2*3).
Step 5: Calculate the products. First, calculate 1*4 = 4 and then 2*3 = 6.
Step 6: Subtract the second product from the first. So, 4 - 6 = -2.
