Question

Find a column vector r such that Ar=r where A=[.2 .8 ; .7 .3]. is there any other column vector besides [0 ; 0]?

Answer 1

if you let the column vector r = [a ; b], then this generates two equations in two unknowns.
so there can only be one solution - which is the one you found, i.e. [0 ; 0]

Answer 2

Thank you! So if I need to find a row vector l such that lA = l. The only solution is also [0 0]?

Answer 3

yes - you can prove that algebraically by letting A = [a b ; c d] and letting I = [x ; y] and then trying to solve for x and y. you will always get [0 ; 0]

Answer 4

assuming A is NOT the identity matrix of course.

Answer 5

thanks!

Answer 6

yw