Question

if I had matrix [1 2 0 -1 -3 2 ; 0 0 1 3 -3 1; 0 0 0 1 -1/6 1/2; 0 0 0 0 1 3/11; 0 0 0 0 0 0]. i need to find the general solution of the systemI was given a system of linear equations and told to put it in reduced row echelon form and then find the general solution of the system. I'm not sure how to write each x1 = , x2=

Answer 1

With the given matrix, the system of equations you have is:

`\begin{gathered} x_1+2x_2-x_4-3x_5=2 \\ x_3+3x_4-3x_5=1 \\ x_4-(1)/(6)x_5=(1)/(2) \\ x_5=(3)/(11) \end{gathered}`

Then, you already know x5=3/11.

Now replace these value in the equation above and solve for x4:

`\begin{gathered} x_4-(1)/(6)\cdot(3)/(11)=(1)/(2)^{} \\ x_4-(3)/(66)=(1)/(2) \\ x_4-(1)/(22)=(1)/(2) \\ x_4=(1)/(2)+(1)/(22) \\ x_4=(22+2)/(44)=(24)/(44) \\ x_4=(6)/(11) \end{gathered}`

Now, replace x4 and x5 into the next above equation:

`\begin{gathered} x_3+3\cdot(6)/(11)-3\cdot(3)/(11)=1 \\ x_3+(18)/(11)-(9)/(11)=1 \\ x_3+(9)/(11)=1 \\ x_3=1-(9)/(11)=(11-9)/(11) \\ x_3=(2)/(11) \end{gathered}`