Linear algebra - matrix

[flat marsh]

something tells me that a part of the problem is missing, is there a part you didn't post or is that all?

ok i think i somewhat get it now

do you know when simultaneous equations have infinite number of solutions or no?

so basically in this question you gotta reverse your thought process, you have the answer to the question and you need a problem that suits that answer

yeah exactly

so

we need a matrix A such that it has a rank of 3

its actually very simple

do you understand what a rank means?

no, a rank of 3 basically means that 3 of your equations have to be linearly independent and 1 equation has to be linearly dependent

which basically means the linearly dependent equation has to be a scaled version of one of your independant equations

let me elaborate

i would suggest refining your understanding of ranks & your intuition about linear algebra before you tackle this problem cuz its gonna be really tough if you dont know exactly what ranks mean

3blue1brown has really great videos on this topic