Question

For the following set of simultaneous equations

1.5x - 0.5y = 2

4x + 2y + 3z = 9

7x + y + 5z = 10

• A. The solution is unique
• B. Infinitely many solutions exist
• C. The equations are incompatible
• D. Finite number of multiple solutions exist

Answer 1

The correct option is A The solution is unique

$\left|A\right|=\left|\begin{array}{ccc}1.5& -0.5& 0\\ 4& 2& 3\\ 7& 1& 5\end{array}\right|$

= (1.5)(10-3) + (0.5)(20-21)

= 10.5 - 0.5 = 10 $\ne$ 0
So Rank r=3
Number of unknowns n=3
Hence n = r = 3

$\Rightarrow$ Unique solution.