Element Row Operation problem

**mastermin346** · September 10th 2012, 03:27 AM

Find the value of a , b , c and d.

**kalyanram** · September 10th 2012, 05:52 AM

Consider the augmented matrix $\left( \begin{array}{cccccc}1 & -1 & 0 & 0 & : & 8\\0 & 1 & 1 & 0 & : & 1\\0 & 0 & 1 & 3 & : & 7\\2 & 0 & 0 & -4 & : & 6\\ \end{array} \right)$

$R_4 \rightarrow \frac{R_4 - 2R_1 - 2R_2 + 2R_3}{2}$
$\left( \begin{array}{cccccc}1 & -1 & 0 & 0 & : & 8\\0 & 1 & 1 & 0 & : & 1\\0 & 0 & 1 & 3 & : & 7\\0 & 0 & 0 & 1 & : & 1\\ \end{array} \right)$

$R_3 \rightarrow R_3 - 3R_4$
$\left( \begin{array}{cccccc}1 & -1 & 0 & 0 & : & 8\\0 & 1 & 1 & 0 & : & 1\\0 & 0 & 1 & 0 & : & 4\\0 & 0 & 0 & 1& : & 1\\ \end{array} \right)$

$R_2 \rightarrow R_2 - R_3$
$\left( \begin{array}{cccccc}1 & -1 & 0 & 0 & : & 8\\0 & 1 & 0 & 0 & : & -3\\0 & 0 & 1 & 0 & : & 4\\0 & 0 & 0 & 1 & : & 1\\ \end{array} \right)$

$R_1 \rightarrow R_1 + R_2$
$\left( \begin{array}{cccccc}1 & 0 & 0 & 0 & : & 5\\0 & 1 & 0 & 0 & : & -3\\0 & 0 & 1 & 0 & : & 4\\0 & 0 & 0 & 1 & : & 1\\ \end{array} \right)$

We have

$\left( \begin{array}{cccc}1 & 0 & 0 & 0\\0 & 1 & 0 & 0\\0 & 0 & 1 & 0\\0 & 0 & 0 & 1\\ \end{array} \right)$ $\left( \begin{array}{c}a\\b\\c\\d\\ \end{array} \right)$ = $\left( \begin{array}{c}5\\-3\\4\\1\\ \end{array} \right)$

$a=5, b=-3, c=4, d=1$ .

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