Matrix equation

[Darya]

Hi! So I'm completely new to linear algebra and I'm wondering if I could solve such equation. Division implies inverse matrix but can we find an inverse matrix of a non-square matrix? Are there other ways maybe?
Thaanks!

 

[HallsofIvy]

That matrix equation is equivalent to the system of equations
50a+200b+ 50c= 10; 50a+ 50b+ 200c= 100
50d+ 200e+ 50f= 200; 50d+ 50e+ 200f= 50
50g+ 200h+ 50i= 100; 50g+ 50h+ 200f= 250

Yes, that is 6 equations in 9 unknowns. No, that cannot be solved. There are not enough equations.

 

[Darya]

That matrix equation is equivalent to the system of equations
50a+200b+ 50c= 10; 50a+ 50b+ 200c= 100
50d+ 200e+ 50f= 200; 50d+ 50e+ 200f= 50
50g+ 200h+ 50i= 100; 50g+ 50h+ 200f= 250

Yes, that is 6 equations in 9 unknowns. No, that cannot be solved. There are not enough equations.

thought so, appreciate your answer!