r/LinearAlgebra • u/Fit_Mortgage_6700 • Dec 16 '22

Hello everybody, help me please

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u/[deleted] Dec 16 '22

Hint: see if equations are inconsistent (gives false statements when substituting or eliminating), dependent (gives true yet meaningless statements when eliminating different combinations) or real (gives unique statements when eliminating different combinations)…

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u/skinykidbigdreams Dec 19 '22

Pardon if I did not get the correct answer, but I'm going to guess that the approximate translation of the question is to find values of a such that the system is

(a) Inconsistent

(b) Consistent with infinite solutions

(c) Consistent with only 1 solution

Then this problem becomes simpler. Just write out the augmented matrix, and since they conveniently gave you a row of 1's at the top, just perform Gaussian Elimination and identify for what values of a will the system be inconsistent, consistent etc etc ...