MATH221 December 2011
• Q1 (a) • Q1 (b) • Q2 (a) • Q2 (b) • Q3 (a) • Q3 (b) • Q4 (a) • Q4 (b) • Q5 (a) • Q5 (b) • Q6 (a) • Q6 (b) • Q7 • Q8 (a) • Q8 (b) •
Question 08 (a)
|
Consider the matrix
a) Find a basis for the column space of A.
|
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?
|
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!
|
Hint
|
How can the row reduced version of A help you find the column space?
|
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.
- If you are stuck on a problem: Read the solution slowly and as soon as you feel you could finish the problem on your own, hide it and work on the problem. Come back later to the solution if you are stuck or if you want to check your work.
- If you want to check your work: Don't only focus on the answer, problems are mostly marked for the work you do, make sure you understand all the steps that were required to complete the problem and see if you made mistakes or forgot some aspects. Your goal is to check that your mental process was correct, not only the result.
|
Solution
|
Found a typo? Is this solution unclear? Let us know here. Please rate my easiness! It's quick and helps everyone guide their studies.
The basis of the column space of A are the columns of A corresponding to the linearly independent columns of the row-reduced version of A. We will find the row reduced matrix for A by performing Gaussian elimination as follows:
Add row 1 to row 3; subtract row 1 from row 4.
.
Add twice row 2 to row 3.
.
Multiply row 3 by 1/3.
.
Subtract twice row 3 from row 1; add row 3 to row 4
.
The row reduced version of A has columns 1, 2, and 4 as linearly independent vectors. Therefore, the basis of the column space will be the first, second and fourth column of the original matrix A. Hence a basis for the column space is:
.
|
Click here for similar questions
MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Matrix operations, Pages using DynamicPageList3 parser function, Pages using DynamicPageList3 parser tag
|
Math Learning Centre
- A space to study math together.
- Free math graduate and undergraduate TA support.
- Mon - Fri: 12 pm - 5 pm in LSK 301&302 and 5 pm - 7 pm online.
Private tutor
|