Evaluate the following system of equation by Gaussian Elimination method x1+5×2+2×3=9 x1+x2+7×3=6 -3×2+4×3=-2

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Augmented matrix

A=(152  9117  60−34  −2)A=begin{pmatrix}
1 & 5 & 2 & 9
1 & 1 & 7 & 6
0 & -3 & 4 & -2
end{pmatrix}A=⎝⎛​110​51−3​274​  9  6  −2​⎠⎞​

R2=R2−R1R_2=R_2-R_1R2​=R2​−R1​

(152  90−45  −30−34  −2)begin{pmatrix}
1 & 5 & 2 & 9
0 & -4 & 5 & -3
0 & -3 & 4 & -2
end{pmatrix}⎝⎛​100​5−4−3​254​  9  −3  −2​⎠⎞​

R2=−R24R_2=-dfrac{R_2}{4}R2​=−4R2​​

(152  901−5/4  3/40−34  −2)begin{pmatrix}
1 & 5 & 2 & 9
0 & 1 & -5/4 & 3/4
0 & -3 & 4 & -2
end{pmatrix}⎝⎛​100​51−3​2−5/44​  9  3/4  −2​⎠⎞​

R1=R1−5R2R_1=R_1-5R_2R1​=R1​−5R2​

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