Question

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

Answer 1

a)

`\begin{gathered} A=\begin{pmatrix}8 & 4 \\ 10 & 6 \\ 6 & 4\end{pmatrix} \\ B=\begin{pmatrix}103 \\ 249\end{pmatrix} \end{gathered}`

b)

Dimension A = 3 x 2

Dimension B = 2 x 1

c)

Cost of credits

Sean $1820

Kevin $2524

Bill $1614

`\begin{pmatrix}Sean \\ \: Kevin \\ \: Bill\end{pmatrix}\begin{pmatrix}1820 \\ \: 2524 \\ \: 1614\end{pmatrix}`

Explanation:

With the help of the statement, we create the matrices A and B:

`\begin{gathered} A=\begin{pmatrix}8 & 4 \\ 10 & 6 \\ 6 & 4\end{pmatrix}\rightarrow3*2 \\ B=\begin{pmatrix}103 \\ 249\end{pmatrix}\rightarrow2*1 \end{gathered}`

Now, we calculate the product just like this:

`\begin{gathered} \text{Product }A\cdot B=\begin{pmatrix}8\cdot103+4\cdot249 \\ 10\cdot103+6\cdot249 \\ 6\cdot103+4\cdot249\end{pmatrix}=\begin{pmatrix}1820 \\ \: 2524 \\ \: 1614\end{pmatrix} \\ \text{Product }A\cdot B=\begin{pmatrix}Sean \\ Kevin \\ Bill\end{pmatrix}\begin{pmatrix}1820 \\ 2524 \\ 1614\end{pmatrix} \end{gathered}`