Find the determinant of the matrix \( D = \begin{pmatrix} 1 & 2 \\ 3 & 4
Practice Questions
Q1
Find the determinant of the matrix \( D = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \). (2019)
-2
2
4
0
Questions & Step-by-Step Solutions
Find the determinant of the matrix \( D = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \). (2019)
Step 1: Identify the elements of the matrix D. The matrix D is given as D = [[1, 2], [3, 4]]. This means the first row has elements 1 and 2, and the second row has elements 3 and 4.
Step 2: Use the formula for the determinant of a 2x2 matrix. The formula is Det(D) = (a * d) - (b * c), where a, b, c, and d are the elements of the matrix arranged as follows: D = [[a, b], [c, d]]. In our case, a = 1, b = 2, c = 3, and d = 4.
Step 3: Substitute the values into the formula. We have Det(D) = (1 * 4) - (2 * 3).
Step 4: Calculate the products. First, calculate 1 * 4 = 4. Then calculate 2 * 3 = 6.
Step 5: Subtract the second product from the first. So, we have 4 - 6 = -2.
Step 6: Write down the final result. The determinant of the matrix D is -2.
