Question

The produce manager at a market orders 10 lb of​ tomatoes, 20 lb of​ zucchini, and 40 lb of onions from a local farmer one week. ​
A) Write a 1times3 matrix A that represents the amount of each item ordered. ​
B) The following​ week, the produce manager increases his order by​ 10%. Find a matrix B that represents this order.
​C) Find AplusB and tell what the entries represent.

Answer 1

Answer:

(A) $A=\left[\begin{array}{ccc}10&20&40\end{array}\right]$

(B) $B=\left[\begin{array}{ccc}11&22&44\end{array}\right]$

(C) $A+B=\left[\begin{array}{ccc}21&42&84\end{array}\right]$

Step-by-step explanation:

The manager ordered 10 lb of​ tomatoes, 20 lb of​ zucchini, and 40 lb of onions from a local farmer one week.

(A)

Matrix A represents the amount of each item ordered. ​It is 1 × 3 matrix.

Then matrix A is:

$A=\left[\begin{array}{ccc}10&20&40\end{array}\right]$

(B)

Next week the manager increases the order of all the products by 10%.

Then the amount of new orders are:

Tomatoes $=10\times [1+\frac{10}{100}]=10\times1.10=11$

Zucchini $=20\times [1+\frac{10}{100}]=20\times1.10=22$

Onions $=40\times [1+\frac{10}{100}]=40\times1.10=44$

Th matrix B represents the amount of each order for the next week. Then matrix B is:

$B=\left[\begin{array}{ccc}11&22&44\end{array}\right]$

(C)

Add the two matrix A and B as follows:

$A+B=\left[\begin{array}{ccc}10&20&40\end{array}\right]+\left[\begin{array}{ccc}11&22&44\end{array}\right]\\=\left[\begin{array}{ccc}(10+11)&(20+22)&(40+44)\end{array}\right]\\=\left[\begin{array}{ccc}21&42&84\end{array}\right]$

The entries of the matrix (A + B) represent the amount of tomatoes, zucchini and onions ordered for two weeks.