Question

The system of equation, if a b are arbitrary numbers x+2y-3z- a 2x+4y-6z 2a+2 has (A) No solutions regardless of values of a and b (B) Infinitely many solutions regardless of values of a and b (C) a unique solution if a b-0 D) a unique solution regardless of values of a and b

Answer 1

(A) No solutions regardless of values of a and b.

Explanation:

Asumming that the system of equations is
`x+2y-3z=a\\ 2x+4y-6z=2a+2`, the corresponding augmented matrix of the system is
`\left[\begin{array}{cccc}1&2&-3&a\\2&4&-6&2a+2\end{array}\right]`.

If two time the row 1 is subtracted to row 1, we get the following matrix

`\left[\begin{array}{cccc}1&2&-3&a\\0&0&0&2a+2-2a\end{array}\right]`.

Then the system has no solutions regardless of values of a and b.