Example 4

Let A = 2i - 5j, B = i + 3j.

(a) Find A + B, A - B, -A, and 6B.

A + B = (2 + 1)i + (-5 + 3)j = 3i - 2j. A - B = (2 - 1)i + (-5 - 3)j = i - 8j.

-A= (-1)A = f(-1)2i + (-1)(-5)j = -2i + 5j, 6B = 6(i + 3j) = 6i + 18j.

(b) Find the vector D such that 3A + 5D = B.

5D = -3A + B,

D = 1/5 (-3A + B).

= 1/5 (-3 · 2 + 1)i + 1/5 (-3 · (-5) + 3)j,

= -i + 18/5 j.