Question

Question 11: The system$\left[\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 0& 0& 0\end{array}\right]\stackrel{\mathbf{R}}{\mathbf{x}}\mathbf{=}\left[\begin{array}{c}1\\ 2\\ 3\end{array}\right]$ is inconsistent.

Short answer

Answer:

True, the given system of equation is inconsistent.

Step-by-step solution

Corresponding augmented matrix

In the given We have given the system of equation is$\left[\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 0& 0& 0\end{array}\right]\stackrel{}{\mathrm{x}}=\left[\begin{array}{c}1\\ 2\\ 3\end{array}\right]$ .

Augmented matrix with respect to given equation will be.$\left[\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 0& 0& 0\end{array}\right]\left[\begin{array}{c}1\\ 2\\ 3\end{array}\right]$

Justification of answer

From the augmented matrix we can see there is no solution to the system of equation. Because for any value of vector x the$0\ne 3$ .

Hence, the system of equation has no solution.

Final answer

True, given system of equation is inconsistent.