augmented matrix

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[frank meteor]

what property is it supposed to have

the system of equation it represents has no solution?

[tranquil zealot]

Correct

Well that’s what I’m supposed to prove

[frank meteor]

for all lambda?

[tranquil zealot]

yes

[frank meteor]

the rank of the left 3 columns should be less than 3

[tranquil zealot]

I need to prove the system is inconsistent

[frank meteor]

but the determinant of them is not always 0
so i think you are finding lambda

[tranquil zealot]

I don’t understand what a determinant or rank is

[frank meteor]

uhh

what tools do you have available

[tranquil zealot]

Tools in what context

What do you mean by tools

[frank meteor]

what do you know about matrices

[tranquil zealot]

not much honestly i’ve only just started learning about matrices last month

[frank meteor]

i guess what you could do is replace each row with an equation in x,y,z, then solve for x,y,z, (in terms of lambda) and then you should have a division by 0 problem when the system is inconsistent

[tranquil zealot]

i’m a first year uni student

Okay i’ll try that, thank you

Is there any point in the process of working out where i’d have to use a free variable do you think?

[frank meteor]

depends how you solve systems of equations, but probably not?

[tranquil zealot]

wdym division by 0 problem

At what point will there be a division by 0 problem

I need to reduce the matrix to row echelon form