Write the vector form of the general solution of the given system of linear equations.x_1+4x_4=0 , x_2-2x_4

glamrockqueen7 2021-09-30 Answered

Write the vector form of the general solution of the given system of linear equations.
\(x_1+4x_4=0\)
\(x_2−2x_4\)

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Expert Answer

coffentw
Answered 2021-10-01 Author has 14785 answers

\(\begin{bmatrix}1&0&4&0 \\0&1&-2&0 \end{bmatrix}\) Rewrite the corresponding augmented matrix of the system of linear equations.
\(\begin{bmatrix}1&0&4&0 \\0&1&-2&0 \end{bmatrix}\)Transform the matrix in its reduced row echelon form.
\(x_1=-4x_4\)
\(x_2=2x_4\)
\(x_4=x_4\) free
Determine the general solution.
\([x_1,x_2,x_4]=x_4[-4,2,1]\) Express the solutions in vector form.

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