Purchase Solution

Linear Algebra : Vectors - Inner Products

Not what you're looking for?

Ask Custom Question

Given a vector w, the inner product of R^n is defined by:
<x,y>=Summation from i=1 to n (xi,yi,wi)

[a] Using this equation with weight vector w=(1/4,1/2,1/4)^t to define an inner product for R^3 and let x=(1,1,1)^T and y=(-5,1,3)^T

Show that x and y are orthogonal with respect to this inner product. Compute the values of ||x|| and ||y|| with respect to this inner product.

[b]In C[0,1], with inner product defined above, consider the vectors 1 and x. Find the angle theta between 1 and x. Determine the vector projection p of 1 onto x and verify that 1-p is orthogonal to p.

Thank you.

Purchase this Solution

Solution Summary

Inner products are calculated and vector relations proven.
The solution is detailed and well presented.

Purchase this Solution


Free BrainMass Quizzes
Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Probability Quiz

Some questions on probability