Question

If `bara = bari + 2 barj , barb = - 2 bari + barj , barc = 4 bari + 3 barj ` find x and y such that `barc = x bara + y barb.`

Answer 1

Given, ` bar c = x bara + y barb`
or ` 4 bari + 3 barj = x (bari + 2 barj) + y (-2bari + barj)`
or ` 4 bari + 3 barj = (x - 2 y) bari + (2x + y) barj`
Comparing both the sides, we get
` x - 2y = 4`
and ` 2x + y = 3`
Solving the equations , we get
x = 2 and y = - 1