Set
x = [0 : 4,4,-4. 1. 1]' and y = ones(9, 1)
(a) Use the MATLAB function norm to compute the values of ||x||, ||y||, ||x + y|| and to verify that the triangle inequality holds. Use MATLAB also to verify that the parallelogram law
||x + y||2 + ||x - y||2 = 2(||x||2 + ||y||2)
is satisfied.
(b) If

then why do we know that |t| must be less than or equal to 1? Use MATLAB to compute the value of t and use the MATLAB function acos to compute the angle between x and y. Convert the angle to degrees by multiplying by 180/Ï€. (The number n is given by pi in MATLAB.)
(c) Use MATLAB to compute the vector projection p of x onto y. Set z = x - p and verify that z is orthogonal to p by computing the scalar product of the two vectors. Compute ||x||2 and ||z||2 + ||p||2 and verify that the Pythagorean Law is satisfied.

Transcribed Image Text:

x'y ||x|| |ly|