# Finite mathematics

*label*Other

*timer*Asked: Sep 16th, 2013

**Question description**

**True or False**

**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. **

**1. 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. Suppose the straight lines represented by a system of two linear equations in two variablesare parallel to each other. Then the system has infinitely many solutions. **

**3. If A and B are matrices of the same order, then (A + B)r = Ar + Br **

**4. If A and B are matrices such that AB and BA are both defined, then A and B must be squarematrices. **

**5. If A is a square matrix with inverse A ^{-1} and c is a nonzero real number, then (cA)^{-1} = 1/c A^{-1}**

**6. If AX= B is a system of n linear equations in n unknowns and A**

^{-1}**does not**

**exist, then**

**AX= B does not have a unique solution.**