First slide

System of linear equations

Question

The system of equations
      $- 2 x + y + z = a$
       $x - 2 y + z = b$
       $x + y - 2 z = c$
has

Difficult

A

No solution if $a + b + c \neq 0$
B

Unique solution if $a + b + c = 0$
C

Infinite number of solutions if $a + b + c = 0$
D

none of these

Solution

When we add three equations, we get $0 = a + b + c$ .
Thus, the system does not have a solution if $a + b + c \neq 0$ .

If $a + b + c = 0$ , the system has infinite number of solutions given by

                  $x = \frac{1}{3} (3 k - 2 a - b)$

                  $y = \frac{1}{3} (3 k - a - 2 b)$

                 $z = k$

Where $k \in C$ .

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