1. Equality of matrices.
What condition(s) must be checked to verify that two matrices are equal?
Reflections 4.7 Reflect on your understanding
In addition to the reflection activities below, re-read Section 4.2 Terminology and notation. Be sure you understand each of the new definitions introduced in this chapter, and spend some time committing them to memory.
2. Matrix operations.
(a)
For each, describe in one sentence (in words, not formulas!) how to carry out the operation.
- matrix addition
- matrix subtraction
- scalar multiplication
- transpose
(b)
Briefly describe (in words, not formulas!) how to carry out matrix multiplication. (This one might take more than one sentence.)
3. Systems via matrix equations.
Explain how the operation of matrix multiplication combined with the concept of matrix equality allows an entire system of linear equations to be represented as a single matrix equation
4. Context of operation symbols and notation.
In this chapter we have introduced a number of new mathematical operations, but in most cases were are using old symbols and notation to represent these new operations. It is important to be able to use the context in which these symbols and notation appear to determine exactly what operation is represented.
(a)
(b)
(c)
5. Domain of matrix multiplication.
(a)
What condition(s) must two matrices meet in order for their product to be defined?
(b)
6. Old rules no longer apply.
(a)
Explain why the commutative rule
(b)
(c)
Explain why the binomial expansion rule
(d)
Explain why the expression
(e)
Can the expression
7. Number of solutions for a homogeneous systems.
(a)
Explain in terms of matrix algebra why it is true that every homogeneous system
(b)
In the algebra of numbers we have the rule that if
