Question

14. Let R^2 have inner product defined by ((x1,x2), (y,, y2)) 4x1y1 +9x2y2 A. Determine the norm of (-1,2) in this space B. Determine the norm of (3,2) in this space.

Answer 1

The norm of a vector
`\vec x` is equal to the square root of the inner product of
`\vec x` with itself.

a.
`\|(-1,2)\|=√(\langle(-1,2),(-1,2)\rangle)=√(4(-1)^2+9(2)^2)=√(40)=2√(10)`

b.
`\|(3,2)\|=√(\langle(3,2),(3,2)\rangle)=√(4(3)^2+9(2)^2)=√(72)=6\sqrt2`