# Linear Algebra Problems

1. Mar 17, 2013

### matqkks

Linear Algebra Problems
Are there any resources consisting of a collection of problems on linear algebra for students to practice? I am looking for good interesting problems which test students’ understanding. These questions or examples should be for teaching rather than just testing. The level of difficulty is first year undergraduate.

2. Mar 17, 2013

### KarlBu

mathworksheetsgo.com

3. Mar 17, 2013

### Mdhiggenz

Let me know if you find any matqkks. I too am interested.

4. Mar 22, 2013

### Sankaku

Last edited by a moderator: May 6, 2017
5. Sep 25, 2013

### s11004799

I am looking for help in this question."Rather than using the standard definitions of addition and scalar multiplication in R^3, suppose the operation is define as follows: (c1,y1,z1,) + (x2,y2,z2) = (x1+x2+1,y1+y2+1,z1+z2+1)

c(x,y,z) = (cx,cy,cz)
With this new definitions, is a vector space?

6. Sep 30, 2013

### HallsofIvy

Staff Emeritus
Determine whether or not this addition (the scalar multiplication defined is just the usual one on $R^3$) has the properties required for addition in a vector space:
1) u+ v= v+ u (commutativity)
2) (u+ v)+ w= u+ (v+ w) (associativity)
3) There exist a specific vector, O, such that v+ O= O+ v= v for any vector v (O is NOT necessarily (0, 0, 0)).
4) For any vector v, there exist a vector, u, such that v+ u= u+ v= O.
5) For any number, a, and vectors u and v, a(u+ v)= au+ av. (Distributive)

7. Sep 30, 2013