Given-that-p-3i-4j-q-2i-j-and-r-5i-j-Express-vector-r-intrems-of-p-and-q-

Question Number 150362 by otchereabdullai@gmail.com last updated on 11/Aug/21

Given that p = (3 i + 4 j), q = (2 i - j) and

r = 5 i - j . Express vector r intrems of

p and q .

Answered by mr W last updated on 11/Aug/21

s a y r = a p + b q

(\begin{matrix} 5 \\ - 1 \end{matrix}) = [\begin{matrix} 3 & 2 \\ 4 & - 1 \end{matrix}] (\begin{matrix} a \\ b \end{matrix})

(\begin{matrix} a \\ b \end{matrix}) = {[\begin{matrix} 3 & 2 \\ 4 & - 1 \end{matrix}]}^{- 1} (\begin{matrix} 5 \\ - 1 \end{matrix})

= \frac{1}{11} [\begin{matrix} 1 & 2 \\ 4 & - 3 \end{matrix}] (\begin{matrix} 5 \\ - 1 \end{matrix}) = (\begin{matrix} \frac{3}{11} \\ \frac{23}{11} \end{matrix})

\Rightarrow r = \frac{3}{11} p + \frac{23}{11} q

c h e c k :

\frac{3}{11} \times 3 + \frac{23}{11} \times 2 = 5 ✓

\frac{3}{11} \times 4 - \frac{23}{11} \times 1 = - 1 ✓

Commented by otchereabdullai@gmail.com last updated on 11/Aug/21

God bless you prof W