# Finite mathematics

**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.**

## Tutor Answer

Brown University

1271 Tutors

California Institute of Technology

2131 Tutors

Carnegie Mellon University

982 Tutors

Columbia University

1256 Tutors

Dartmouth University

2113 Tutors

Emory University

2279 Tutors

Harvard University

599 Tutors

Massachusetts Institute of Technology

2319 Tutors

New York University

1645 Tutors

Notre Dam University

1911 Tutors

Oklahoma University

2122 Tutors

Pennsylvania State University

932 Tutors

Princeton University

1211 Tutors

Stanford University

983 Tutors

University of California

1282 Tutors

Oxford University

123 Tutors

Yale University

2325 Tutors