Answer to Question #206276 in Statistics and Probability for mishal rafiq

Question

(b) Global Insurance Company has four salespeople working in Hill town. The number of policies sold during the last month is given in matrix A, as 

o1 Malley Coponi Steomberg Deutsch

8 7 6 8 Automobile

6 9 11 5 Life

A= 4 3 2 0 Health

0 2 1 3 Homeowners

i) Let S= [1 1 1 1]. Find SA and interpret its elements.

ii) Find 𝐴𝑆௧ and interpret its elements. 

Answer 1

$A=\begin{bmatrix}8&7&6&8\\6&9&11&5\\4&3&2&0\\0&2&1&3\end{bmatrix}$

$(1) SA=\begin{bmatrix} 1&1&1&1\end{bmatrix} \begin{bmatrix}8&7&6&8\\6&9&11&5\\4&3&2&0\\0&2&1&3\end{bmatrix} =\begin{bmatrix} 18&21&20&16\end{bmatrix}$

       Elements are 18,21,20 and 16.In this case we get a horizontal matrix of order 1x4.

$(2) AS^T=\begin{bmatrix}8&7&6&8\\6&9&11&5\\4&3&2&0\\0&2&1&3\end{bmatrix} \begin{bmatrix} 1\\1\\1\\1\end{bmatrix} =\begin{bmatrix} 18\\21\\20\\16\end{bmatrix}$

    Its elements are same as the above AS matrix.In this we get a vertical matrix of order 4 x 1.