MAT 223 Winter 2023
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MAT 223
Winter 2023
1. (Fundamentals) Complete the following.
(a) Explain the differences between the scalar zero and the zero vector. Explain using several sentences and examples.
(b) Discuss with your group row reduction using an augmented matrix (Appendix 2). Using
your own example with 3 equations and 3 unknowns, demonstrate how row reduction works. Make sure to explain what the final results mean in terms of the original problem.
2. Let 
= l 1(1) . Find vectors 
1 and 
2 such that 
is a linear combination of 
1 and 
2 . Additional 3
conditions are that 
1 , 
2 should be non-zero vectors that are not multiples of each other. (In other words, make it mathematically interesting.) Explain your thinking using complete sentences.
3. This problem is about different ways to express a plane. First, choose a mathematically interesting plane that can be expressed as the solution set to ax + by + cz = d (this is called Cartesian form). By interesting we mean a plane that is not overly simple (e.g. z = 0) where the plane helps your group illustrate key features of vector forms and the process of finding them.
(a) Express your plane in vector form. Show all your work and explain each step.
(b) In your own words, explain the advantages of expressing a plane in vector form.
2023-02-02