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5 votes
Find the determinant of the elementary matrix. (Assume k ≠ 0.)

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User Baleb
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8.5k points

1 Answer

6 votes

Final answer:

The determinant of an elementary matrix is equal to the scalar used to transform the original matrix.

Step-by-step explanation:

The determinant of an elementary matrix can be found by taking the determinant of the original matrix and multiplying it by the determinant of the elementary matrix. Since the student didn't provide the specific elementary matrix, let's consider a simple example.

Let's say we have the 2x2 identity matrix, I. If we multiply the second row of I by a scalar k, we get the elementary matrix E. To find the determinant of E, we can multiply the determinant of I by k, since the determinant of E is k times the determinant of I.

The determinant of I is 1, so the determinant of E would be k. Therefore, the determinant of the elementary matrix E is k.

answered
User Nathan Fellman
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8.3k points
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