Solve the system of equations (Use matrices.):x-2y+z = 16, 2x-y-z = 14, 3x+5y-4z =-10

shadsiei 2021-02-02 Answered

Solve the system of equations (Use matrices.):
x2y+z=16,
2xyz=14,
3x+5y4z=10

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Expert Answer

wheezym
Answered 2021-02-03 Author has 103 answers

Step 1
Given,
x2y+z=16,
2xyz=14,
3x+5y4z=10
Step 2
Consider the Augmented matrix is of the form AX=B
[121211354][xyz]=[161410]
Here,
A=[121211354],X=[xyz] and B=[161410]
Use Gauss Elimination method,
Consider,
[A/B]=[121162111435410]
R2R22R1
[121160331835410]
R3R33R1
[1211603318011758]
R213R2
[121160116011758]
R3R311R2
[1211601160048]
R314R3
[1211601160012]
Step 3
The above matrix is in the row echelon form
By back substitution we get,
z=2(i)
yz=6(ii)
x2y+z=16(iii)
Substitute the value of z in (ii) we get,
y2=6
y=4
Substitute the value of y and z in (iii) we get,
x2(4)+2=16
x+8+2=16
x+10=16
x=1610
x=6
Therefore the solution set is (x,y,z)=(6,4,2)

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Jeffrey Jordon
Answered 2022-01-29 Author has 2313 answers

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