Yes, these values satisfy the given conditions.cummings12332 said:Homework Statement
find a norm on R2 for which||(0,1)||=1=||(1,0)|| but ||(1,1)||=0.000001
Homework Equations
hints: ||(a,b)|| = A |a+b|+B|a-b
The Attempt at a Solution
by the hints i have A+B=1 and 2A=0.000001
then solved the equations system i get A=0.0000005 B=1-A=0.9999995 then ||(a,b)|| = 0.000001|a+b|+0.9999995 |a-b|
is it the answers?
The norm of a vector is the length or magnitude of the vector. It is calculated by taking the square root of the sum of the squares of the vector's components.
R2, also known as the Euclidean plane, is a 2-dimensional coordinate system where points are represented by an ordered pair of numbers (x, y).
This notation means that the norm of the vector (0,1) is equal to 1.
To find the norm of a vector, you can use the Pythagorean theorem. Square each component of the vector, add them together, and then take the square root of the sum.
In this context, it means that the norm of the vector (1,1) is very close to 0. This could indicate that the vector is nearly parallel to the x-axis or y-axis, but not exactly.