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Q2E

Expert-verifiedFound in: Page 265

Book edition
5th

Author(s)
Otto Bretscher

Pages
442 pages

ISBN
9780321796974

**Use Gaussian elimination to find the determinant of the matrices A in Exercises 1 through 10.**

**2. ${\left[\begin{array}{ccc}1& 2& 3\\ 1& 6& 8\\ -2& -4& 0\end{array}\right]}$**

Therefore, the determinant of given matrix is given by,

$detA=24$

Gaussian elimination method is used to solve a system of linear equations.

Gaussian elimination provides a relatively efficient way of constructing the inverse to a matrix.

Interchanging two rows. Multiplying a row by a constant (any constant which is not zero).

Given Matrix,

${A}{=}{\left[}\begin{array}{ccc}1& 2& 3\\ 1& 6& 8\\ -2& -4& 0\end{array}{\right]}$

First, we multiply the first row by -1 and add it to the second row. Then, we multiply the first row by 2 and add it to the third row.

We get,

$A=\left[\begin{array}{ccc}1& 2& 3\\ 0& 4& 5\\ 0& 0& 6\end{array}\right]$

We had zero row swaps, so

role="math" localid="1659503688412" $\mathrm{det}\mathrm{A}={(-1)}^{0}.1.4\xb76\phantom{\rule{0ex}{0ex}}\mathrm{det}\mathrm{A}=24$

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