Answer to Question #160387 in Linear Algebra for Saba tariq

Question #160387

Find solution of equation by using the gaussian elimination method.

2x+3y+z=2

-x+2y+2z=1

x-y-2z=-1



1
Expert's answer
2021-02-04T08:05:21-0500

The augmented matrix for the set of equations is:

[231212211121]\begin{bmatrix} 2 & 3 & 1 & 2 \\ -1 & 2 & 2 & 1 \\ 1 & -1 & -2 & -1 \end{bmatrix}

Rearranging the rows:

[112123121221]\begin{bmatrix} 1 & -1 & -2 & -1 \\ 2 & 3 & 1 & 2 \\ -1 & 2 & 2 & 1 \end{bmatrix}

Multiply the first row by -2 and add it to the second row:

[112105541221]\begin{bmatrix} 1 & -1 & -2 & -1 \\ 0 & 5 & 5 & 4 \\ -1 & 2 & 2 & 1 \end{bmatrix}

Add the first row to the third row:

[112105540100]\begin{bmatrix} 1 & -1 & -2 & -1 \\ 0 & 5 & 5 & 4 \\ 0 & 1 & 0 & 0 \end{bmatrix}

The third row translates to:

y=0y=0

Therefore, the second row translates to:

5z=45z=4

z=4/5z=4/5

The first row then translates to:

x2(4/5)=1x-2(4/5)=-1

x8/5=1x-8/5=-1

x=1+8/5x=-1+8/5

x=3/5x=3/5


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