Answer
(a) $u+v=7i+2j$
(b) $u-v=-3i-4j$
(c) $4u=8i-4j$
(d) $3v+5u=25i+4j$
Work Step by Step
(a) $u+v=(2i-j)+(5i+3j)=(2+5)i+(-1+3)j=7i+2j$
(b) $u-v=(2i-j)-(5i+3j)=(2-5)i+(-1-3)j=-3i-4j$
(c) $4u=4(2i-j)=4(2i)+4(-j)=8i-4j$
(d) $3v+5u=3(5i+3j)+5(2i-j)=3(5i)+3(3j)+5(2i)+5(-j)=15i+9j+10i-5j=25i+4j$
