Indicate whether the statement is always true or sometimes false. If it is somet
ID: 2965098 • Letter: I
Question
Indicate whether the statement is always true or sometimes false. If it is sometimes false, please show a counterexample.
Indicate whether the statement is always true or sometimes false. If it is sometimes false, please show a counterexample. (a) A linear system of one equation in two unknown must be consistent. (b) If the number of equations in a linear system exceeds the number of unknowns, the system must be inconsistent (c) A homogeneous linear system of two equations in three unknowns has infinitely many solutions (d) If the reduced row echelon form of the augmented matrix for a linear system has a row of zero, then the system must have infinitely many solutions.Explanation / Answer
Only the statement (b) is false. Here is a counterexample:
x+y=1
x-y=3
3x+y=5
The above system has 3 equations but 2 unknowns. However, it is consistent, as x=2 and y=-1 is a solution.