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Q17E

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

**Find the determinant in Exercise 17, where \[\left| {\begin{aligned}{*{20}{c}}{\bf{a}}&{\bf{b}}&{\bf{c}}\\{\bf{d}}&{\bf{e}}&{\bf{f}}\\{\bf{g}}&{\bf{h}}&{\bf{i}}\end{aligned}} \right| = {\bf{7}}\].**

**17. \[\left| {\begin{aligned}{*{20}{c}}{{\bf{a}} + {\bf{d}}}&{{\bf{b}} + {\bf{e}}}&{{\bf{c}} + {\bf{f}}}\\{\bf{d}}&{\bf{e}}&{\bf{f}}\\{\bf{g}}&{\bf{h}}&{\bf{i}}\end{aligned}} \right|\]**

Hence, \[\left| {\begin{aligned}{*{20}{c}}{a + d}&{b + e}&{c + f}\\d&e&f\\g&h&i\end{aligned}} \right| = 7\].

At row 1, add \[ - 1\] time row 2 to row 1 to obtain:

\[\left| {\begin{aligned}{*{20}{c}}{a + d}&{b + e}&{c + f}\\d&e&f\\g&h&i\end{aligned}} \right| = \left| {\begin{aligned}{*{20}{c}}a&b&c\\d&e&f\\g&h&i\end{aligned}} \right|\]

The statement is \[\left| {\begin{aligned}{*{20}{c}}a&b&c\\d&e&f\\g&h&i\end{aligned}} \right| = 7\].

Therefore,

\[\left| {\begin{aligned}{*{20}{c}}{a + d}&{b + e}&{c + f}\\d&e&f\\g&h&i\end{aligned}} \right| = 7\]

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