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Math Help - Forming System of equations for matrices from a word problem

  1. #1
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    Forming System of equations for matrices from a word problem

    19. An investment firm offers 3 stock portfolios: A, B and C. The number of blocks of each type of stock
    in each of these portfolios is as follows:
    Portfolio
    A B C
    High 6 1 3
    Med 3 2 3
    Low 1 5 3
    Suppose a client wants 26 blocks of high-risk stock, 25 blocks of moderate-risk stocks, and 29 blocks
    of low-risk stock. Determine the number of each portfolio that should be suggested to the client by
    solving the appropriate system of equations.

    my attempt:
    I got a 1x3 Matrix with 3 variables x, y, z multiplied by the 3x3 matrix above, but when i try to solve i get a messed up answer.. any help is appreciated
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  2. #2
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    Hello, s0urgrapes!

    Must be your algebra . . . The answers come out nicely.


    19. An investment firm offers 3 stock portfolios: A, B and C. The number
    of blocks of each type of stock in each of these portfolios is as follows:

    . . . . . \text{Portfolio}
    \begin{array}{c|ccc}<br />
& A & B & C \\ \hline<br />
\text{High} & 6 & 1 & 3 \\<br />
\text{Med} & 3 & 2 & 3 \\<br />
\text{Low} & 1 & 5 & 3 \end{array}


    Suppose a client wants 26 blocks of high-risk stock,
    25 blocks of moderate-risk stocks, and 29 blocks of low-risk stock.

    Determine the number of each portfolio that should be suggested
    to the client by solving the appropriate system of equations.

    We have: . \begin{bmatrix} 6 & 1 & 3 \\ 3 & 2 & 3 \\ 1 & 5 & 3\end{bmatrix}\begin{bmatrix}A\\B\\C\end{bmatrix} \;=\;\begin{bmatrix}26\\25\\29\end{bmatrix} \qquad\Rightarrow\qquad \begin{bmatrix}A\\B\\C\end{bmatrix}\;=\;\begin{bma  trix}1\\2\\6\end{bmatrix}

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