Linear algebra

[dim river]

Need help understanding how to prove this

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[dim river]

I'm not sure how to approach this

[swift lintel]

for the first one you have

x1 = -58 + lambda * (-13)

can you write this as x1 = -6 + gamma * (13)

for some suitable chosen gamma

then figure out if you can pick gamma for the entire vector

you are proving set inclusion, i assume you are familiar with vector arithmetic

@dim river

[dim river]

I don't quite understand your solution, do you mean x1 = (-58 -101 9 0) + c(-13 -25 2 1) where c is a scalar?

[warm fractal]

yes

that's what span means

[dim river]

I don't understand how I can use that to prove the above statement, I'm missing something conceptually which I can't figure out what?

[warm fractal]

have you worked with "a == b mod n" before

i assume it's a yes as you are in university

[dim river]

In cs yes

but I dont see the correlation

[warm fractal]

from "a == b mod n" can we infer that "a-b is a multiple of n"

and whats span{v}? all linear combinations of v i.e. all multiples of v.

you must see the similarity now

(a+tb)+tc == a+te mod t

get it now?

[dim river]

im still confused lol, cuz after solving them I get something like x1 + x2 = 4

How does this prove that x belongs to both solution sets

@swift lintel @warm fractal

[warm fractal]

man just use the fact that span{v} = x+span{v} for any x in span{v}

[dire bay]

$x\in y + \text{span}{v} \iff$ there exists scalar $k$ such that $x = y + kv$