Question

For the following set of simultaneous equations 1.5x-0.5y=2,   4x+2y+3z=9,   7x+y+5=10.

(a) The solution is unique

(b) Infinitely many solutions exist

(c) The equations are incompatible

(d) Finite number of multiple solutions exist

The question was posed to me during an internship interview.

My doubt is from Basics of Linear Algebra in portion Linear Algebra Overview of Signals and Systems

Answer 1

Right answer is (a) The solution is unique

For explanation: The equations can be written as \(\begin{bmatrix}

1.5 & -0.5 & 0\\

4 & 2 & 3\\

7 & 1 & 5\\

\end{bmatrix}\)

It can also be written as A = \(\begin{bmatrix}

3 & -2 & 0\\

4 & 2 & 3\\

7 & 1 & 5\\

\end{bmatrix}\),  |A|=19

Hence, it has a unique solution.