Write the system of linear equations in the form Ax = b and solve this matrix equation for x. begin{cases}x_1+x_2-3x_3=-1-x_1+2x_2=1x_1-x_2+x_3=2end{cases}

Daniaal Sanchez 2020-11-09 Answered
Write the system of linear equations in the form Ax = b and solve this matrix equation for x.
{x1+x23x3=1x1+2x2=1x1x2+x3=2
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Expert Answer

Clara Reese
Answered 2020-11-10 Author has 120 answers
Firstly, switch to matrix form.
[113120111][x1x2x3]=[112]
Now, form augmented matrix and by Gaussian climination reach row reduced echelon form.
Form augmented matrix [113112011112]
R2+R1 and R3R1R3 [113103300243]
R2/3R2  [113103300243]
R1R2R2 and R3+2R2R3 and R3/3R3[10210101.50011.5]
R1+2R3R1 and R2+R3R2 [10020101.50011.5]
From here, we have solution.
x1=2x2=1.5x3=1.5
Result: x1=2x2=1.5x3=1.5
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