Question

By using gauss elimination method the following system of equation is 6x-y-z=19,3x+4y+z=26,x+2y+6z=22
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Answer 1

Answer:

6x-y-z=19

3x+4y+z=26

x+2y+6z=22

Answer 2

Concept:

Gauss elimination method is also called as the row reduction algorithm for solving system of linear equations. It has a sequence of operations which are performed on the corresponding matrix of coefficients. We can also use this method to estimate the rank of the given matrix.

Given:

We are given the system of linear equations as:

6 x - y - z = 19

3 x + 4 y + z = 26

x + 2 y + 6 z = 22

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Find:

We need to solve the system of equations by gauss elimination method.

Solution:

We have:

6 x - y - z = 19

3 x + 4 y + z = 26

x + 2 y + 6 z = 22

Writing these equations in matrix form:

$\left[\begin{array}{ccc}6&-1&-1\\3&4&1\\1&2&6\end{array}\right]\left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}19\\26\\22\end{array}\right]$

Row reducing the matrix, we get:

$\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]\left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}4\\3\\2\end{array}\right]$

So, from this, we get that:

x=4

y=3

z=2.

Therefore, after solving the system of equations by gauss elimination method, we get that x=4, y=3 and z=2.

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