Find a matrix that gives the increase or decrease in sales.

[dcc3038026]

Carney and Dobler sell auto and hazard insurance. Their sales, in dollars, for the months of July and August are given in the following matrices.

Auto____Hazard
July
22,000 - 45,000 Carney
19,000 - 27,000 Dobler
August
25,000 - 41,000 Carney
14,000 - 21,000 Dobler

Find a matrix that gives the increase (decrease) in sales by each salesman for each type of insurance from July to August.

 

[mmm4444bot]

Where is the information that assigns these figures to a particular salesperson?

 

[dcc3038026]

Here is the info.......

Carney and Dobler sell auto and hazard insurance. Their sales, in dollars, for the months of July and August are given in the following matrices.

Auto____Hazard
July
22,000 - 45,000 Carney
19,000 - 27,000 Dobler
August
25,000 - 41,000 Carney
14,000 - 21,000 Dobler

Find a matrix that gives the increase (decrease) in sales by each salesman for each type of insurance from July to August.

 

[Deleted member 4993]

Here is the info.......

Carney and Dobler sell auto and hazard insurance. Their sales, in dollars, for the months of July and August are given in the following matrices.

Auto____Hazard
July
22,000 - 45,000 Carney
19,000 - 27,000 Dobler
August
25,000 - 41,000 Carney
14,000 - 21,000 Dobler

Find a matrix that gives the increase (decrease) in sales by each salesman for each type of insurance from July to August.

Please define matrix in the context - according to text book/class notes.

 

[mmm4444bot]

Matrix multiplication ...

Hi DCC:

As Subhotosh posted, I'm also not sure what this exercise entails.

In the meantime, if you're familiar with matrix multiplication and factors for percent-change, then you can write a matrix equation whose solution is the set of percentages (positive for increase and negative for decrease).

The following is a trivial journey, since it's much more straightforward to write the equations directly ...

A percent-change factor is 1 + r, where r is the percent in decimal form.

If we let w represent the percent-change in Carney's auto sales from July to August, then the percent-change factor is 1+w.

If we let x represent the percent-change in Carney's hazard sales from July to August, then the percent-change factor is 1+x.

If we let y represent the percent-change in Dobler's auto sales from July to August, then the percent-change factor is 1+y.

If we let z represent the percent-change in Dobler's auto sales from July to August, then the percent-change factor is 1+z.

Here is a matrix equation that you could solve to find the percents w, x, y, and z.

\(\displaystyle \left[ \begin{array}{cccc} 22 & 0 & 0 & 0 & 0 & 45 & 0 & 0 & 0 & 0 & 19 & 0 & 0 & 0 & 0 & 27 \end{array} \right] \cdot \left[ \begin{array}{c} 1 + w & 1 + x & 1 + y & 1 + z \end{array} \right] \;=\; \left[ \begin{array}{c} 25 & 41 & 14 & 21 \end{array} \right]\)

Or, you could tell us what your teacher expects.

Cheers,

~ Mark