Find the determinant of the matrix D = [[4, 2], [3, 1]]. (2023)
Practice Questions
Q1
Find the determinant of the matrix D = [[4, 2], [3, 1]]. (2023)
-2
2
10
12
Questions & Step-by-Step Solutions
Find the determinant of the matrix D = [[4, 2], [3, 1]]. (2023)
Step 1: Identify the elements of the matrix D. The matrix D is [[4, 2], [3, 1]].
Step 2: Label the elements of the matrix. Let a = 4, b = 2, c = 3, d = 1.
Step 3: Use the formula for the determinant of a 2x2 matrix, which is det(D) = (a * d) - (b * c).
Step 4: Substitute the values into the formula: det(D) = (4 * 1) - (2 * 3).
Step 5: Calculate the first part: 4 * 1 = 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 D is -2.
Determinant of a 2x2 Matrix – The determinant of a 2x2 matrix is calculated using the formula ad - bc, where the matrix is represented as [[a, b], [c, d]].
