What is the determinant of the matrix \( \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \)?
Practice Questions
1 question
Q1
What is the determinant of the matrix \( \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \)?
-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: What is the determinant of the matrix \( \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \)?
Solution: The determinant is calculated as \( 1*4 - 2*3 = 4 - 6 = -2 \).
Steps: 6
Step 1: Identify the elements of the matrix. The matrix is \( \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \). The elements are: a = 1, b = 2, c = 3, d = 4.
Step 2: Use the formula for the determinant of a 2x2 matrix, which is given by \( ad - bc \).
Step 3: Substitute the values into the formula. Here, a = 1, b = 2, c = 3, d = 4, so we calculate: \( 1*4 - 2*3 \).
Step 4: Perform the multiplication: \( 1*4 = 4 \) and \( 2*3 = 6 \).
Step 5: Subtract the second result from the first: \( 4 - 6 = -2 \).
Step 6: The determinant of the matrix is \( -2 \).
