Theory question 108
VectorsGiven that p = (5, 3), q = (−1, 2), r = (17, 5) (column vectors) and r = αp + βq, where α and β are scalars, express q in terms of r and p.
Show the model answer
Model answer
5α − β = 17 and 3α + 2β = 5. Doubling the first and adding: 13α = 39, α = 3, β = −2.
r = 3p − 2q, so q = ½(3p − r).
Explanation
Compare the top and bottom components.