Question

Let vector 'v' = (1,1) and vector 'w' = (1,-1).

a)Find real numbers t1 and t2 such that t1(v) + t2(w) = (13,-12).

b)Find real numbers t1 and t2 such that t1(v) + t2(w) = (x1,x2)for any x1,x2 that is an element of R.

Answer 1

t1(1,1) + t2(1,-1) = (13,-12)

(t1,t1) + (t2,-t2) = (13,-12)

(t1+t2 , t1 -t2) = (12, -12)

so
t1+t2 = 13
t1-t2 = -12
add them
2t1 = 1
t1 = 1/2

subtract them
2t2 = 25
t2 = 25/2

b) using he results of above
replace 13 with x1 and -12 with x2 and repeat my steps