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Expert-verified Found in: Page 165 ### Linear Algebra and its Applications

Book edition 5th
Author(s) David C. Lay, Steven R. Lay and Judi J. McDonald
Pages 483 pages
ISBN 978-03219822384 # Compute the determinants of the elementary matrices given in Exercise 25-30.28. \left( {\begin{aligned}{*{20}{c}}k&0&0\\0&1&0\\0&0&1\end{aligned}} \right).

The determinant of the matrix is $$k$$.

See the step by step solution

## Step 1: Compute the determinant of the elementary matrix

If A is a triangular matrix, then according to theorem 2, det A is the product of the entries on its main diagonal.

The determinant of the matrix is the product of the diagonal entries because the matrix is triangular.

\begin{aligned}{c}\left| {\begin{aligned}{*{20}{c}}k&0&0\\0&1&0\\0&0&1\end{aligned}} \right| = \left( k \right)\left( 1 \right)\left( 1 \right)\\ = k\end{aligned}

Thus, the determinant of the matrix is $$k$$. ### Want to see more solutions like these? 