Use the​ Gauss-Jordan method to solve the system of equations. If the system has infinitely many​ solutions, give the solution with z arbitrary.x-5y+2z=13x-4y+2z=-1

Ramsey 2021-02-19 Answered

Use the​ Gauss-Jordan method to solve the system of equations. If the system has infinitely many​ solutions, give the solution with z arbitrary.
x5y+2z=1
3x4y+2z=1

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Expert Answer

Caren
Answered 2021-02-20 Author has 96 answers

Step 1
To find the solution of system of equations reduce the matrix [AB] where A is the matrix formed by the coefficients of LHS of the equations and B is the matrix formed by the RHS of the equations.
Step 2
Find the matrix [AB] from the given system of equations and row reduce it.
[15213421]R2R23R1
[152101144]R2R211
[152101411411]R1R1+5R2
[1021191101411411]
Step 3
Form the equation from the above matrix.
x+211z=911
y411z=411
Step 4
Let z=t. Find the value of x and y.
x+211(t)=911
x=9112t11
y411(t)=411
y=411+4t11
Step 5
Answer: For random z=t the solution set will be,
{(9112t11,411+4t11),t}

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