Problem: If is a real number, then the simultaneous system has no solution if and only if is equal to
Answer Choices:
A.
B.
C.
D. or
E.
Solution:
If , then elementary operations an the system yields an equivalent system which is a solution of the given system. If , adding the equations we get the inconsistency .
Alternately, the general condition that the matrix of the coeficients of the syatem and the augmented matrix must have equal or unequal rank for consistency or inconsistency applies when or respectively.