Honey C.

asked • 02/15/23

Solve the given system of linear equation using Gauss-Jordan elimination.

Z3 +Z4 + Z5 = 0

2Z1 + 2Z2 - Z3 + Z5 = 0

Z1 + Z2 - 2Z3 - Z5 = 0

-Z1 - Z2 + 2Z3 - 3Z4 + Z5 = 0

Luke J.

I see 4 equations and 5 unknowns, it is not a solvable system of equations for all independent variables, it will most likely end with exactly 1 variable being dependent on exactly 1 other variables value. Please provide the 5th equation or confirm that what you posted above is all that there was to be posted. Thank you.
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02/16/23

Honey C.

Yes, I confirm this is all that was given/posted. Thank you.
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02/17/23

1 Expert Answer

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Aarav B. answered • 16d

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CS undergrad at Purdue University with an emphasis

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We can use RREF to solve this.

The augment matrix is:

[[0, 0, 1, 1, 1, 0],

[2, 2, -1, 0, 1, 0],

[1, 1, -2, 0, -1, 0],

[-1, -1, 2, -3, 1, 0]]


We can perform RREF on this to get:

[[1, 1, 0, 0, 1, 0],

[0, 0, 1, 0, 1, 0],

[0, 0, 0, 1, 0, 0],

[0, 0, 0, 0, 0, 0]]


Z2 and Z5 are both free variables.


Z1 = -s - t

Z2 = s

Z3 = -t

Z4 = 0

Z5 = t

s and t are both parameters



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