What is the determinant of the matrix \( G = \begin{pmatrix} 2 & 3 \\ 5 &
Practice Questions
Q1
What is the determinant of the matrix \( G = \begin{pmatrix} 2 & 3 \\ 5 & 7 \end{pmatrix} \)? (2023)
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Questions & Step-by-Step Solutions
What is the determinant of the matrix \( G = \begin{pmatrix} 2 & 3 \\ 5 & 7 \end{pmatrix} \)? (2023)
Step 1: Identify the elements of the matrix G. The matrix G is given as G = [[2, 3], [5, 7]]. This means the first row has elements 2 and 3, and the second row has elements 5 and 7.
Step 2: Use the formula for the determinant of a 2x2 matrix. The formula is: determinant = (first element * second element of the second row) - (second element * first element of the second row).
Step 3: Plug in the values from the matrix into the formula. Here, the first element is 2, the second element of the second row is 7, the second element is 3, and the first element of the second row is 5.
Step 4: Calculate the first part of the formula: 2 * 7 = 14.
Step 5: Calculate the second part of the formula: 3 * 5 = 15.
Step 6: Subtract the second part from the first part: 14 - 15 = -1.
