Question

suppose a company is testing the flexibility of new type of fiberglass by creating a diving board out of the fiberglass machine

Answer 1

The three equations are as you are using:

`\begin{gathered} a+b+c=116 \\ 8a+4b+c=448 \\ 27a+9b+c=972 \end{gathered}`

So by solving the system of linear equations:

`\begin{bmatrix}{1} & {1} & {1} \\ {8} & {4} & {1} \\ {27} & {9} & {1}\end{bmatrix}\begin{bmatrix}{a} & {} & {} \\ {b} & {} & \\ {c} & & {}\end{bmatrix}=\begin{bmatrix}{116} & {} & {} \\ {448} & {} & \\ {972} & & {}\end{bmatrix}`

Now i'm telling you to use transformation and then solve it. it'll be easy for you:

The first transformation is:

`R_2-8R_1=R_2`

Then:

`R_3-27R_1=R_3_{}_{}`

And then

`R_3-(9)/(2)R_2=R_3`

Then you'll get:

`\begin{gathered} a+b+c=116 \\ -4b-7c=-480 \\ (11)/(2)c=0 \end{gathered}`