# Matrix Solution

March 07, 2019

**The Matrix Solution**

**Given the following system of equations, write the associated augmented matrix.**

2*x* + 3*y* – *z* = 6

–*x* – *y* – *z* = 9

*x* + *y* + 6*z* = 0

Write down the coefficients and the answer values, including all "minus" signs. If there is "no" coefficient, then the coefficient is "1".

That is, given a system of (linear) equations, you can relate to it the matrix (the grid of numbers inside the brackets) which contains only the coefficients of the linear system. This is called "an augmented matrix": the grid containing the coefficients from the left-hand side of each equation has been "augmented" with the answers from the right-hand side of each equation.

The entries of (that is, the values in) the matrix correspond to the *x*-, *y*- and *z*-values in the original system, as long as the original system is arranged properly in the first place. Sometimes, you'll need to rearrange terms or insert zeroes as place-holders in your matrix.

**Given the following system of equations, write the associated augmented matrix.**

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*x* + *y* = 0

*y* + *z* = 3

*z* – *x* = 2

I first need to rearrange the system as:

*x* + *y* = 0

*y* + *z* = 3

–*x* + *z* = 2

Then we can write the associated matrix as:

**The reverse problem: Given the following augmented matrix, write the associated linear system.**

Remember that matrices require that the variables be all lined up nice and neat. And it is customary, when you have three variables, to use *x*, *y*, and *z*, in that order. So the associated linear system must be:

*x*** + 3 y = 4**

2

2

*y*–*z*= 5

3

3

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