Where Can I Find Linear Algebra Practice Problems for First Year Undergraduates?

[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.

 

[KarlBu]

mathworksheetsgo.com

 

[Mdhiggenz]

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

 

[Sankaku]

The Schaum's outline series is decent for worked problems. On a slightly higher level is the Halmos problem book:
https://www.amazon.com/dp/0883853221/?tag=pfamazon01-20

Hefferon's free textbook has a solutions manual:
http://joshua.smcvt.edu/linearalgebra/

 

[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?
Justify your answers

 

[HallsofIvy]

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)

 

[whiteheadj]

The examples sheets for the Cambridge Linear Algebra course contain some excellent questions. They can be found here.

In particular, the "Preliminary example sheet" (essentially a revision sheet) might be just what you seek.