Answer to Question #292570 in Linear Algebra for Hamza Khan

Question

Question 1. Let u = (2,1,0,5) e R². Apply the process of inner product spaces.

• Solve u for its length
• Solve u for its Normalized vector

Answer 1

1] The length of u is;

$\displaystyle \|u\|=\sqrt{u\cdot u}=[(2,1,0,5)\cdot(2,1,0,5)]^{\frac{1}{2}}=[2\times2+1\times1+0\times0+5\times5]^{\frac{1}{2}}\\ \qquad\ =[4+1+0+25]^{\frac{1}{2}}=\sqrt{30}$

2] The normalized vector of u is;

$\displaystyle \frac{u}{\|u\|}=\frac{1}{\sqrt{30}}(2,1,0,5)$