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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
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
.
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 square matrix with inverse
.
and c is a nonzero real number, then
6.True or false: If AX = B is a system of n linear equations in n unknowns and
AX = B does not have a unique solution.
does not exist, then
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