We can regard a 2 1 as either a vector or a 1 times 2 matri

We can regard a = [2, 1] as either a vector or a 1 times 2 matrix. This means we can compute the 1-norm, the 2-norm and the infinity norm for a as a vector, as well as the matrix norm of a. Is the matrix norm equal to any of the vector norms? Which one? Repeat the question for b = [2 1] 16. (a) Show that the Eucidean norm of a vector v is given by a formula similar to that for the matrix norm: ||v|| = max_x notequalto 0 x middot v/||x||,

Solution

Norm 1 of vector A is the maximum sum of absolute column, hence the norm 1 of vector A will be equal to 2

Norm infinity of vector A will also be equal to 2

Norm 2 of vector A will be sqrt( (2)^2 + (1)^2 ) = sqrt5)

The 2 norm is equivalent to the distance between the point (x,y)