The given matrix is the augmented matrix for a system of linear equations. Give the vector form for the general solution. displaystyle{left[begin{matrix}{1}&{0}&-{1}&-{2}{0}&{1}&{2}&{3}end{matrix}right]}

Ava-May Nelson 2020-11-08 Answered
The given matrix is the augmented matrix for a system of linear equations. Give the vector form for the general solution.
[10120123]
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Expert Answer

Theodore Schwartz
Answered 2020-11-09 Author has 99 answers
The given matrix is
B=[10120123]
Reduce the given augmented matrix B in to system of linear equation
Ax=b
The matrix form of the first equation is
[101012][x1x2x3]=[23]
where
A=[101012],x=[x1x2x3],b=[23]
We use another equation to find a. general solution
x1x3=2(3)
x2+2x3=3(4)
x3=x3(5)
Then
(3)x1=2+x3
(4)x2=32x3
(5)x3=x3
In vectors form, the general solution, we obtain
x=[x1x2x3]=[2+x332x3x3]=[230]+x3[121]
answer x=[230]+x3[121]
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