Question

Write the system below in the form AX=B. Then solve the system by entering A and B into a graphing utility and computing

Answer 1

We are given the system

`\begin{gathered} x\text{ -3y+z=8} \\ 3x+4y+2z=\text{ -17} \\ 4x\text{ -4y +2z= -2} \end{gathered}`

to write this system of the form

`Ax=b`

where A is a matrix, x is a vector and b is another vector, we simply take each equation and write it in matrix form. The first equation is

`x\text{ -3y+z=8}`

so, we will take a look at the left hand side of the equality sign. We have

`x\text{ -3y+z}`

we will take a look at the coefficients of each variable and write that as the first row of the matrix. That would be the row 1 -3 1 as the coefficient of x and z is 1 and the coefficient of y is -3. For b, the first row would be simply the number 8. So, if we do the same with the other two equations, we have

`A=\begin{bmatrix}{1} & {\text{ -3}} & {1} \\ {3} & {4} & {2} \\ {4} & {\placeholder{⬚}\text{ -4}} & {2}\end{bmatrix}`

and

`b=\begin{bmatrix}{8} & {\placeholder{⬚}} & {\placeholder{⬚}} \\ {\placeholder{⬚}\text{ -17}} & {\placeholder{⬚}} & {\placeholder{⬚}} \\ {\text{ -2}} & {\placeholder{⬚}} & {\placeholder{⬚}}\end{bmatrix}`

By using any of the two methods of the question (the use of software is beyond the scope of the session) we get that the solution is

`\begin{gathered} x=\frac{\placeholder{⬚}\text{ -19}}{3} \\ y=\frac{\text{ -}8}{3} \\ z=(19)/(3) \end{gathered}`