Write the vector form of the general solution of the given system of linear equations. x_1+2x_2-x_3+x_4=0

sjeikdom0 2021-09-18 Answered
Write the vector form of the general solution of the given system of linear equations.
x1+2x2−x3+x4=0

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Plainmath recommends

  • Ask your own question for free.
  • Get a detailed answer even on the hardest topics.
  • Ask an expert for a step-by-step guidance to learn to do it yourself.
Ask Question

Expert Answer

Jaylen Fountain
Answered 2021-09-19 Author has 7191 answers

\([1,2,-1,1,0]\) Write the augmented matrix of the coefficients and constants
\([1,2,-1,1,0] \)Transform the matrix in its reduced row echelon form.
x1=-2x2+x3-x4
x2=x2 free
x3=x3 free
x4=x4 free
Determine the general solution
\(\begin{bmatrix}x_1 \\x_2 \\x_3 \\x_4 \end{bmatrix}=x_2\begin{bmatrix}-2 \\1 \\0 \\0 \end{bmatrix}+x_3\begin{bmatrix}1 \\0 \\0 \\0 \end{bmatrix}-x_4\begin{bmatrix}-1 \\0 \\0 \\1 \end{bmatrix}\)Rewrite the solution in vector form

Have a similar question?
Ask An Expert
5
 

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more
...