Algebraic Operations on Matrices - Properties of Scalar Multiplication of a Matrix

Two farmers Ramakishan and Gurucharan Singh cultivate only three varieties of rice namely Basmati, Permal and Naura. The sale (in rupees) of these varieties of rice by both the farmers in the month of September and October are given by the following matrices A and B

September sales (in Rupees)

${\displaystyle \text{A}=\left[\begin{array}{ccc}10000& 20000& 30000\\ 50000& 30000& 10000\end{array}\right]\left[\begin{array}{c}\text{Ramakrishan}\\ \text{Guruvharan}\end{array}\right]}$

October sales (in Rupees)

${\displaystyle \text{B}=\left[\begin{array}{ccc}5000& 10000& 6000\\ 20000& 10000& 10000\end{array}\right]\left[\begin{array}{c}\text{Ramakrishan}\\ \text{Guruvharan}\end{array}\right]}$

• What is the value of A₂₃?

Manufacture produces three stationery products Pencil, Eraser and Sharpener which he sells in two markets. Annual sales are indicated below

If the unit Sale price of the Pencil, Eraser, and Sharpener is Rs. 2.50, Rs. 1.50 and Rs. 1.00 respectively, and the unit cost of the above three commodities is Rs. 2.00, Rs. 1.00 and Rs. 0.50 respectively, then,

Based on the above information answer the following:

• Profit in market A and B respectively are ____________.

Find x and y, if  ${\displaystyle 2\left[\begin{array}{cc}1& 3\\ 0& x\end{array}\right]+\left[\begin{array}{cc}y& 0\\ 1& 2\end{array}\right]=\left[\begin{array}{cc}5& 6\\ 1& 8\end{array}\right]}$

Manufacture produces three stationery products Pencil, Eraser and Sharpener which he sells in two markets. Annual sales are indicated below

If the unit Sale price of the Pencil, Eraser, and Sharpener is Rs. 2.50, Rs. 1.50 and Rs. 1.00 respectively, and the unit cost of the above three commodities is Rs. 2.00, Rs. 1.00 and Rs. 0.50 respectively, then,

Based on the above information answer the following:

• Total revenue of market A?

Two farmers Ramakishan and Gurucharan Singh cultivate only three varieties of rice namely Basmati, Permal, and Naura. The sale (in rupees) of these varieties of rice by both the farmers in the month of September and October are given by the following matrices A and B

September sales (in Rupees)

${\displaystyle \text{A}=\left[\begin{array}{ccc}10000& 20000& 30000\\ 50000& 30000& 10000\end{array}\right]\left[\begin{array}{c}\text{Ramakrishan}\\ \text{Guruvharan}\end{array}\right]}$

October sales (in Rupees)

${\displaystyle \text{B}=\left[\begin{array}{ccc}5000& 10000& 6000\\ 20000& 10000& 10000\end{array}\right]\left[\begin{array}{c}\text{Ramakrishan}\\ \text{Guruvharan}\end{array}\right]}$

• If Ramkishan receives 2% profit on gross sales, compute his profit for each variety sold in October.

Manufacture produces three stationery products Pencil, Eraser and Sharpener which he sells in two markets. Annual sales are indicated below

If the unit Sale price of the Pencil, Eraser, and Sharpener is Rs. 2.50, Rs. 1.50 and Rs. 1.00 respectively, and the unit cost of the above three commodities is Rs. 2.00, Rs. 1.00 and Rs. 0.50 respectively, then,

Based on the above information answer the following:

• Total revenue of market B?

Let ${\displaystyle A=\left[\begin{array}{cc}2& 4\\ 3& 2\end{array}\right],B=\left[\begin{array}{cc}1& 3\\ -2& 5\end{array}\right],C=\left[\begin{array}{cc}-2& 5\\ 3& 4\end{array}\right]}$

Find  3A - C

Two farmers Ramakishan and Gurucharan Singh cultivate only three varieties of rice namely Basmati, Permal and Naura. The sale (in rupees) of these varieties of rice by both the farmers in the month of September and October are given by the following matrices A and B

September sales (in Rupees)

${\displaystyle \text{A}=\left[\begin{array}{ccc}10000& 20000& 30000\\ 50000& 30000& 10000\end{array}\right]\left[\begin{array}{c}\text{Ramakrishan}\\ \text{Guruvharan}\end{array}\right]}$

October sales (in Rupees)

${\displaystyle \text{B}=\left[\begin{array}{ccc}5000& 10000& 6000\\ 20000& 10000& 10000\end{array}\right]\left[\begin{array}{c}\text{Ramakrishan}\\ \text{Guruvharan}\end{array}\right]}$

• The total sales in September and October for each farmer in each variety can be represented as ____________.