Ma170 Assignment 2 Week 2

MA170 Assignment 2 week 2

Part 1A

What is the difference between scalar multiplication and matrix multiplication?  Give examples of each operation. (150 words or less)

Scalar multiplication is the sort we learn about in grade school. It is one number multiplied by another. It is an alternative to repeated addition. Scalar multiplication is always commutative (a*b = b*a). Example   54* = 4*5 = 20  Matrix multiplication is an operation defined on rectangular arrays of numbers that meet certain requirements as to the array dimensions. A matrix of m rows and n columns may multiply one that is n rows and p columns. The values of m and p need not be anything in particular, and are often the same. The result of the multiplication is a matrix with m rows and p columns. In general, matrix multiplication is not commutative. (A•B ≠ B•A)  Use of the term "number" in the above descriptions should be considered to include numeric constants, variables, and/or algebraic expressions.

True or False

Part 1B

If you think the statement is true, then show that it is true. On the other hand, if you think the statement is false, then give an example that disproves the statement. For example, the statement "If A and B are matrices of the same order, then A - B = B - A" is false and an example that disproves it is

For 

while 

Such an example is called a counterexample.

1. True or false: A system comprising two linear equations in two variables has a unique solution if and only if the straight lines represented by the equations are nonparallel

2. True or false: Suppose the straight lines represented by a system of two linear equations in two variables are parallel to each other. Then the system has infinitely many solutions.

3. True or false: If A and B are matrices of the same order, then (A+B)T = AT+ BT

4. True or false: If A and B are matrices such that AB and BA are both defined, then A and B must be square matrices.

5. True or false: If A is a...