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Give an example of a matrix, then calculate its determinant using elementary row operations!
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Q. Give an example of a matrix, then calculate its determinant using elementary row operations!
- Choose Matrix A: Choose a matrix. Let's take the matrix .
- Subtract to Eliminate: To find the determinant using elementary row operations, first, we'll subtract times the first row from the second row to make the element at position zero.New matrix A = \left[\begin{array}{cc}\(\newline\)\(1\) & \(2\) (\newline\)\(0\) & \(-2\)\(\newline\)\end{array}\right]\( (since \)\(3\) - \(3\)\times\(1\) = \(0\)\( and \)\(4\) - \(3\)\times\(2\) = \(-2\)).
- Calculate Determinant: Now, the determinant of matrix can be calculated as the product of the diagonal elements (since the other element in the second row is zero).Determinant = .
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