Write the vector form of the general solution of the given system of linear equations.x_1+3x_2+2x_4=0, x_3-6x_4=0

Chardonnay Felix 2021-09-19 Answered
Write the vector form of the general solution of the given system of linear equations.
x1+3x2+2x4=0
x3−6x4=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

i1ziZ
Answered 2021-09-20 Author has 4496 answers

\(\begin{bmatrix}1 & 0 & 3 & 2 & 0 \\0 & 0 & 1 & -6 & 0 \end{bmatrix}\) Rewrite the corresponding augmented matrix of the system of linear equations.
\(\begin{bmatrix}1 & 3 & 0 & 2 & 0 \\0 & 0 & 1 & -6 & 0 \end{bmatrix}\)Transform the matrix in its reduced row echelon form.
x1=-3x2-2x4
x2=x2 free
x3=6x4
x4=x4 free
Determine the general solution.
\(\begin{bmatrix}x_1 \\x_2 \\x_3 \\x_4 \end{bmatrix}=x_2\begin{bmatrix}-3 \\1 \\0 \\0 \end{bmatrix}+x_4\begin{bmatrix}-2 \\0 \\6 \\1 \end{bmatrix}\) Express the solutions in vector form."

Have a similar question?
Ask An Expert
26
 

Expert Community at Your Service

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