Is the following equation regarded as a linear equation? 0 x 1 </msub> +

Question

Is the following equation regarded as a linear equation?

0 x_{1} + 0 x_{2} + 0 x_{3} = 5

The original question is as below:
Solve the linear system given by the following augmented matrix:

(\begin{array}{cccc} 2 & 2 & 3 & 1 \\ 2 & 5 & 3 & 0 \\ 0 & 0 & 0 & 5 \end{array})

Note the words linear system in the original question. So, I was asking myself whether

0 x_{1} + 0 x_{2} + 0 x_{3} = 5

is a linear equation. Can we call all of the equations given by the matrix collectively as a linear system?

Answer 1

The reason you MUST call it a linear equation is that you want to call the following a linear equation, for all constants

a_{1}, a_{2}, a_{3}

:

a_{1} x_{1} + a_{2} x_{2} + a_{3} x_{3} = 5

You don't want to call this a "sometimes" linear equation.

Answer 2

It is a linear equation with no solutions, so the linear system has no solutions.

Answers (2)