Determinants, system of equations

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@Apu
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Nimboi
NimboiOP5w ago
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Nimboi
NimboiOP5w ago
how? what? 4 unknowns, 3 equations and they solved it? i guess the collinear points condition is the 4th equation to solve for all 4 unknowns but also i'd rather commit seppuku than solve 4 equations in an exam
Opt
Opt5w ago
I'm getting z =0 OR a=1 If we choose z=0, we get x=1 y=1 is always there
Nimboi
NimboiOP5w ago
how are you getting z=0 or a=1 i assume we can't pick variable values and solve the remaining since that's a little illegal
Opt
Opt5w ago
Mb, a=5 or z =0
Nimboi
NimboiOP5w ago
how bru as in where are you getting the values from
Opt
Opt5w ago
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Opt
Opt5w ago
FRACK NO WAIT a=3 or z=0 That should be (-3+a)z=0 I'm effing dumb
Opt
Opt5w ago
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Opt
Opt5w ago
So choose z=0 as your condition and proceed Sub in another equation, get x @Nimboi
Nimboi
NimboiOP5w ago
wait back up what was your first step this was my main doubt a not equal to 3 is fine and all but what then
Opt
Opt5w ago
Gimme a bit. I'll write it down neatly and send.
Nimboi
NimboiOP5w ago
oke the information i derived from the question was i) unique solution - the coefficient determinant not equal to 0 => a is not -3 ii) collinear points - i equated the slope of point A and B to the slope of point B and C which ended up in me getting the equation of a^2 - q^2 = (p - a)(q - p) im just using p,q,r instead of x star y star z star for convenience yeah i got nowhere from there
Opt
Opt5w ago
It's actually -3. My calc is so bad today Basic algebra going weong
Nimboi
NimboiOP5w ago
-3 yeah its all good i got -3 what was wrong here what thought did i skip amazing how the brain is capable of learning things like calculus and quantum physics and still stumbles on basic arithmetic half the time
Opt
Opt5w ago
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Opt
Opt5w ago
Those are technically the star values But whatever
Opt
Opt5w ago
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Opt
Opt5w ago
@Nimboi Got it?
Nimboi
NimboiOP5w ago
oh you can do that? manipulate LHS and RHS at the same time?
Opt
Opt5w ago
Wdym? The augmented matrix?
Nimboi
NimboiOP5w ago
yes i have somehow like never seen that
Opt
Opt5w ago
That's exactly how you're supposed to do it...it's basically adding and subtracting the equations You don't add just the LHS of an equation do you? You add both sides. Basically that, but without the nasty variables and plus and minus signs getting in the way
Nimboi
NimboiOP5w ago
oh oh well i might be dumb
Opt
Opt5w ago
Nah Just go watch a couple Khan Academy vids. They're pretty good when it comes to this topic Search for RREF
Nimboi
NimboiOP5w ago
ah nice okay
Opt
Opt5w ago
Reduced Row Echelon Form Or Gaussian Elimination Same thing
Nimboi
NimboiOP5w ago
pretty cool thank u :> +solved @Opt
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