Find the determinant of \( G = \begin{pmatrix} 4 & 2 \\ 3 & 1 \end{pmatrix} \). (2020)
Practice Questions
1 question
Q1
Find the determinant of \( G = \begin{pmatrix} 4 & 2 \\ 3 & 1 \end{pmatrix} \). (2020)
-2
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The determinant is \( 4*1 - 2*3 = 4 - 6 = -2 \).
Questions & Step-by-step Solutions
1 item
Q
Q: Find the determinant of \( G = \begin{pmatrix} 4 & 2 \\ 3 & 1 \end{pmatrix} \). (2020)
Solution: The determinant is \( 4*1 - 2*3 = 4 - 6 = -2 \).
Steps: 8
Step 1: Identify the elements of the matrix G. The matrix is G = [[4, 2], [3, 1]].
Step 2: Write down the formula for the determinant of a 2x2 matrix. The formula is: det(G) = (a * d) - (b * c), where a, b, c, and d are the elements of the matrix G = [[a, b], [c, d]].
Step 3: Assign the values from the matrix to the variables in the formula. Here, a = 4, b = 2, c = 3, and d = 1.
Step 4: Substitute the values into the determinant formula: det(G) = (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 G is -2.
