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Found in: Page 265

### Linear Algebra With Applications

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,

$detA=24$

See the step by step solution

## Step 1: Definition

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).

## Step 2: Given

Given Matrix,

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

## Step 3: To find determinant by using Gaussian Eliminations

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" $\mathrm{det}\mathrm{A}={\left(-1\right)}^{0}.1.4·6\phantom{\rule{0ex}{0ex}}\mathrm{det}\mathrm{A}=24$

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