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

ringearV

Answered question

2020-12-22

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

Answer & Explanation

Neelam Wainwright

Neelam Wainwright

Skilled2020-12-23Added 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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