Question

If u = <5,2> and v= <4,-3> find 2u +3v

Answer 1

$\vec{u}=[5,\ 2],\ \vec{v}=[4,\ -3]\\\\2\vec{u}=2[5,\ 2]=[(2)(5),\ (2)(2)]=[10,\ 4]\\\\3\vec{v}=3[4,\ -3]=[(3)(4),\ (3)(-3)]=[12,\ -9]\\\\2\vec{u}+3\vec{v}=[10,\ 4]+[12,\ -9]=[10+12,\ 4+(-9)]=[22,\ -5]$