# Solving Linear Algebra Homework: Help Needed!

In summary, the problem involves finding the projection of a vector on the column space of a matrix, using the method of constructing a basis for the subspace and dropping terms involving basis vectors not in the subspace. This can be done if the columns of the matrix are independent vectors. Some equations that may be helpful include ||a|| = sqrt(ATA) and the projection formula shown in the image provided.

## Homework Statement

http://img136.imageshack.us/img136/8452/linalg.png

## Homework Equations

I'm trying to figure out what it's asking me to do, as soon as I figure that out, I maybe be able to figure out the equation...

We've gone over stuff like finding the Vector OQ(->) on something like this..
http://img24.imageshack.us/img24/8452/linalg.png

Anybody have a clue what it's asking?

I've seen equations like;
||a|| = sqrt ( ATA)

and

http://img689.imageshack.us/img689/8452/linalg.png

and some others.. Thanks

Last edited by a moderator:
The "column space" of matrix A is the subspace spanned by its columns. One way to find the projection of a vector on a subspace is:

Construct a basis for the subspace.
Add vectors to extend to a basis for the entire space.
Write your given vector in that basis.

Drop the terms involving basis vectors not in the subspace.

In this case, if the columns themselves are independent vectors, you can use the column vectors as your basis for the subspace.

## 1. What is Linear Algebra?

Linear Algebra is a branch of mathematics that deals with linear equations and their representations in vector spaces. It involves the study of lines, planes, and their higher-dimensional equivalents, and the operations that can be performed on them.

## 2. Why is Linear Algebra important?

Linear Algebra is important because it provides a powerful framework for solving real-world problems in various fields such as science, engineering, economics, and computer graphics. It is also the basis for many advanced mathematical concepts and techniques.

## 3. How do I approach Linear Algebra homework?

The first step in approaching Linear Algebra homework is to understand the problem and identify the relevant concepts and techniques to solve it. Then, break down the problem into smaller, more manageable parts and use the appropriate formulas and methods to solve each part. It is also important to check your work and make sure your answers are accurate.

## 4. What are some common challenges in solving Linear Algebra homework?

Some common challenges in solving Linear Algebra homework include understanding the abstract concepts and properties, applying the correct formulas and methods, and dealing with large and complex systems of equations. It is also important to be careful with calculations and avoid errors.

## 5. Where can I find help for solving Linear Algebra homework?

There are various resources available for help with solving Linear Algebra homework. Your teacher or professor, classmates, and tutors can provide guidance and clarification on specific problems. Online resources such as video tutorials, practice problems, and forums can also be useful. Additionally, there are textbooks and study guides that can provide step-by-step explanations and practice exercises.

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