The row echelon form of a system of linear equations is given. (a) Write the system of equations corresponding to the given matrix. Use x, y, or x, y,

ringearV 2020-12-22 Answered
The row echelon form of a system of linear equations is given.
(a) Write the system of equations corresponding to the given matrix.
Use x, y, or x, y, z, or x1,x2,x3,x4
(b) Determine whether the system is consistent. If it is consistent, give the solution.
10301014320012300000
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Expert Answer

Neelam Wainwright
Answered 2020-12-23 Author has 102 answers
a. The system represented by the matrix is
{x1+3x3=1x2+4x3+3x4=2x3+2x4=30=0
b. This is a consistent system (because the last equation is true for all ordered quadruplets).
The system will not have a single solution, as it is, in effect, a system of THREE equations in FOUR variables.
It is a dependent system.
To solve, we take x4 to be any real number tR, and back-substitute into the other two equations:
Back substitute into (3): [x3+2(t)=0x3=32t]
Back substitute into (2): [x2+4(32t)+3(t)=2x2+128t+3t=2x2+125t=10+5t]
Back substitute into (1): [x1+3(32t)2(t)=1x1+96t=1x1=8+6t]
Result:
a. {x1+3x3=1x2+4x3+3x4=2x3+2x4=30=0
b. Consistent, solution set: {(8+6t,10+5t,32t,t), tR}
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