Question

Sean, Kevin and Bill take classes at both JJC and CSU.Sean takes 8 credits at JJC and 4 credits at CSU; Kevintakes 10 credits at JJC and 6 at CSU; Bill takes 6 credits atJJC and 4 at CSU; the cost per credit at JJC is $103 and atCSU is $249. a) Write a matrix A that gives the credits eachstudent is taking and B that gives the cost per credit at eachschool. b) Find the dimension of A and B. c) Find theproduct AB and the names of its rows and columns.

Answer 1

`\begin{gathered} A=\begin{bmatrix}8 & 4 \\ 10 & 6 \\ 6 & 4\end{bmatrix}_(3*2) \\ B=\begin{bmatrix}103 & 249 \\ \end{bmatrix}_(1*2) \end{gathered}`

1) Notice that there are three students: Sean, Kevin, and Bill and there are 2 schools JJC and CSU. In addition to this, there's the cost per credit. So we can write out the following Matrix A, for the credits:

`\begin{gathered} A=\begin{bmatrix}8 & 4 \\ 10 & 6 \\ 6 & 4\end{bmatrix}_(3*2) \\ \begin{bmatrix}Sean \\ Kevin \\ Bill\end{bmatrix}=\begin{bmatrix}8 & 4 \\ 10 & 6 \\ 6 & 4\end{bmatrix}_(3*2) \end{gathered}`

Note that Matrix A, in this case, works as a table. On the Matrix on the left, we have the name of the students, and at Matrix A, we have each row the credits each student is taking.

2) So now:

`B=\begin{bmatrix}103 & 249 \\ \end{bmatrix}_(1*2)`

Notice that we multiply A by B we'll get the cost for every student.

`\begin{gathered} A=\begin{bmatrix}8 & 4 \\ 10 & 6 \\ 6 & 4\end{bmatrix}_(3*2) \\ B=\begin{bmatrix}103 & 249 \\ \end{bmatrix}_(1*2) \end{gathered}`

And that is the answer.