Question

Which is a coefficient matrix for the system of linear equations?

Answer 1

Answer:

b.

Step-by-step explanation:

e2020

Answer 2

A system is composed by a number of equations, involving a certain number of variables.

The coefficient matrix is a matrix which collects the coefficient of the variable through all the equations, assuming they are written in standard form, i.e.:

- The variable appear in the same order in all the equations;

- The equations are written with all variables on the left hand side and all constant coefficients on the right hand side.

So, first of all, let's rewrite the system in standard form. We'll write a zero coefficient if a variable doesn't appear in the equation, to make things easier for later:

$\begin{cases} 6a+2b+0c=22\\ 0a-8b-3c=-19\\ -10a+0b+9c=-12 \end{cases}$

Now the coefficient matrix can be build simply by considering all coefficients appearing on the left hand sides: the columns represent the variables, the rows represent the equations:

$\left[\begin{array}{ccc}6&2&0\\0&-8&-3\\-10&0&9\end{array}\right]$