Question

Is it possible to write vector (-5,6) as a linear combination of vectors (1,2) and (3,4)

Answer 1

Explanation:

-5i+6j=x(1i+2j)+y(3i+4j)

-5=x+3y(multiply by 2)

6=2x+4y

-10=2x+6y

subtract

16=-2y

y=-8

-5=x+3(-8)

x=-5+24=19

-5i+6j=19(i+2j)-8(3i+4j)

so we can write (-5,6) as a linear combination of (1,2) and (3,4)