What is the determinant of the matrix \( E = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \)?
Practice Questions
1 question
Q1
What is the determinant of the matrix \( E = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \)?
-2
2
4
0
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 \( E = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \)?
Solution: The determinant is calculated as \( 1*4 - 2*3 = 4 - 6 = -2 \).
Steps: 8
Step 1: Identify the elements of the matrix E = [[1, 2], [3, 4]].
Step 2: Recognize the formula for the determinant of a 2x2 matrix, which is det(E) = (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: a = 1, b = 2, c = 3, d = 4.
Step 4: Substitute the values into the determinant formula: det(E) = (1*4) - (2*3).
Step 5: Calculate the first part: 1*4 = 4.
Step 6: Calculate the second part: 2*3 = 6.
Step 7: Subtract the second part from the first part: 4 - 6 = -2.
Step 8: Conclude that the determinant of the matrix E is -2.
