Find the determinant of \( G = \begin{pmatrix} 2 & 3 \\ 5 & 7 \end{pmatrix} \). (2021)
Practice Questions
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Q1
Find the determinant of \( G = \begin{pmatrix} 2 & 3 \\ 5 & 7 \end{pmatrix} \). (2021)
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The determinant is calculated as \( 2*7 - 3*5 = 14 - 15 = -1 \).
Questions & Step-by-step Solutions
1 item
Q
Q: Find the determinant of \( G = \begin{pmatrix} 2 & 3 \\ 5 & 7 \end{pmatrix} \). (2021)
Solution: The determinant is calculated as \( 2*7 - 3*5 = 14 - 15 = -1 \).
Steps: 8
Step 1: Identify the elements of the matrix G. The matrix is G = [[2, 3], [5, 7]].
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 = 2, b = 3, c = 5, and d = 7.
Step 4: Substitute the values into the determinant formula: det(G) = (2 * 7) - (3 * 5).
Step 5: Calculate the first part: 2 * 7 = 14.
Step 6: Calculate the second part: 3 * 5 = 15.
Step 7: Subtract the second part from the first part: 14 - 15 = -1.
Step 8: Conclude that the determinant of the matrix G is -1.
