Question

Given the equations are 4x+2y+z=8, x+ y+ z=3, 3x+y+3z=9. Find the values of x, y and z.

(a) 5/3, 0, 2/3

(b) 1, 2, 3

(c) 4/3, 1/3, 5/3

(d) 2, 3, 4

This question was posed to me in an internship interview.

Origin of the question is Basics of Linear Algebra in section Linear Algebra Overview of Signals and Systems

Answer 1

Correct choice is (a) 5/3, 0, 2/3

Explanation: The matrix from the equations is represented as   M=\(\begin{bmatrix}

4 & 2 & 1\\

1 & 1 & 1\\

3 & 1 & 3\\

\end{bmatrix}\)

The another matrix is X = \(\begin{bmatrix}

8\\

3\\

9\\

\end{bmatrix}\)

Then |M| = 6

For x=\(\begin{bmatrix}

8 & 2 & 1\\

3 & 1 & 1\\

9 & 1 & 3\\

\end{bmatrix}\) = 5/3

Similarly, y=0, z=-2/3.