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Q28Q

Expert-verifiedFound in: Page 165

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 \(k\).

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 \(k\).

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