Register
Solve the system of equations using matrices. Use the Gauss- Jordan elimination method And find a solution set
118k views
4 votes
Solve the system of equations using matrices. Use the Gauss- Jordan elimination method And find a solution set

Solve the system of equations using matrices. Use the Gauss- Jordan elimination method-example-1
User Alessandro Romano
by
3.5k points

1 Answer

3 votes

\begin{gathered} x+y+z=4 \\ x-y-z=0 \\ x-y+z=8 \\ \text{The system using matrix is} \\ \begin{bmatrix}{1} & {1} & {1}, & {4} \\ {1} & {-1} & {-1,} & {0} \\ {1} & {-1} & {1,} & {8}{}{}\end{bmatrix}\rightarrow F2=F2-F1=\begin{bmatrix}{1} & {1} & {1}, & {4} \\ {0} & {-2} & {-2,} & {-4} \\ {1} & {-1} & {1,} & {8}{}{}\end{bmatrix} \\ \rightarrow F3=F3-F1=\begin{bmatrix}{1} & {1} & {1}, & {4} \\ {0} & {-2} & {-2,} & {-4} \\ {0} & {-2} & {0,} & {4}{}{}\end{bmatrix}\rightarrow F2=-(1)/(2)F2 \\ =\begin{bmatrix}{1} & {1} & {1}, & {4} \\ {0} & {1} & {1,} & {2} \\ {0} & {-2} & {0,} & {4}{}{}\end{bmatrix}\rightarrow F3=F3+2F2=\begin{bmatrix}{1} & {1} & {1}, & {4} \\ {0} & {1} & {1,} & {2} \\ {0} & {0} & {2,} & {8}{}{}\end{bmatrix}\rightarrow F3=(1)/(2)F3 \\ =\begin{bmatrix}{1} & {1} & {1}, & {4} \\ {0} & {1} & {1,} & {2} \\ {0} & {0} & {1,} & {4}{}{}\end{bmatrix}\rightarrow F2=F2-F3=\begin{bmatrix}{1} & {1} & {1}, & {4} \\ {0} & {1} & {0,} & {-2} \\ {0} & {0} & {1,} & {4}{}{}\end{bmatrix} \\ \rightarrow F1=F1-F3=\begin{bmatrix}{1} & {1} & {0}, & {0} \\ {0} & {1} & {0,} & {-2} \\ {0} & {0} & {1,} & {4}{}{}\end{bmatrix}\rightarrow F1=F1-F2 \\ =\begin{bmatrix}{1} & {0} & {0}, & {2} \\ {0} & {1} & {0,} & {-2} \\ {0} & {0} & {1,} & {4}{}{}\end{bmatrix} \\ \text{Therefore, the solution is }x=2,\text{ y=-2 and z=4} \end{gathered}

User Richard Nguyen
by
3.4k points
Ask a Question
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

3.6m questions

4.5m answers

Other Questions

A study was completed in Florida. In southern Florida, the study involved 3,000 patients; 54% of them experienced flulike symptoms during the same month. The study had a margin of error of 1.8%. What does
Solve for x in the equation 3 x squared minus 18 x + 5 = 47. (I need this to be an answer like X=3+\_ square root 23)
The sanchez family goes out for dinner, and the price of the meals is $60. The sales tax on the Meals is 7 percent, and they also want to leave a 15 percent tip. What is the total cost of the meal? Analyze
Simplify: 10 ÷ [(5 + 2) − 5]
A survey of 539 adults aged 18-24 year olds was conducted in which they were asked what they did last Friday night. It found: 189 watched TV 163 hung out with friends 29 watched TV and ate pizza, but did
Link Copied!