Question

Need help with this question parts a thru e please

Answer 1

Given:

A statement is given about the sales of ink cartridges by a family owned ink company ABC.

Find:

we have to find the answers of the questions from part(a) to (e) using given statement.

Step-by-step explanation:

(a) Let us represent the number of the Xavier set, Yvonne set and Zena set in the form of x, y and z respectively as following

x = the number of Xavier set

y = the number of Yvonne set

z = the number of Zena set

(b) we can write the given data in following way

Blue Black Red

Xavier(x) 1 1 0

Yvonne(y) 2 3 1

Zena(z) 4 5 1

Left refills 11 14 3

Therefore, the system of linear equations can be represented as

x + 2y + 4z = 11

x + 3y + 5z = 14

0x + y + z = 3

(c) Now we will solve the given system of equations by Gauss-Jordon elimination as below

given system of equation is

x + 2y + 4z = 11

x + 3y + 5z = 14

y + z = 3

The matrix of the above set can be formed as below

`\begin{gathered} \begin{bmatrix}{1} & {2} & {4} \\ {1} & {3} & {5} \\ {0} & {1} & {1}\end{bmatrix}\begin{bmatrix}{x} & {} & {} \\ {y} & {} & {} \\ {z} & {} & {}\end{bmatrix}=\begin{bmatrix}{11} & {} & {} \\ {14} & {} & {} \\ {3} & {} & {}\end{bmatrix} \\ R_2\rightarrow R_2-R_1 \\ \begin{bmatrix}{1} & {2} & {4} \\ {0} & {1} & {1} \\ {0} & {1} & {1}\end{bmatrix}\begin{bmatrix}{x} & {} & {} \\ {y} & {} & {} \\ {z} & {} & {}\end{bmatrix}=\begin{bmatrix}{11} & {} & {} \\ {14} & {} & {} \\ {13} & {} & {}\end{bmatrix} \\ R_3=R_3- \end{gathered}`