Question

You go to the shops on Monday and buy 1 apple, 1 banana, and 1 carrot; the whole transaction totals €15. On Tuesday you buy 3 apples, 2 bananas, 1 carrot, all for €28. Then on Wednesday 2 apples, 1 banana, 2 carrots, for €23. Construct a matrix and vector for this linear algebra system. That is, for A[a/b/c] = [SMon/STue/SWed] Where a, b, c, are the prices of apples, bananas, and carrots. And each s is the total for that day. Fill in the components of A and s. 1 - # Replace A and s with the correct values below: 2. A = [[A11, A12, A13], 3. [A21, A22, A23], 4. [A31, A32, A33]] 5. Run6. S = [Mon, sTue, sWed] 7. Reset

Answer 1

Let A ⇒apple, B⇒ banana and C⇒carrot

Monday ⇒buy 1 apple, 1 banana, and 1 carrot ⇒ all for €15

∴ A + B + C = 15 ⇒ (1)

Tuesday ⇒buy 3 apples, 2 bananas, 1 carrot ⇒ all for €28

∴ 3A + 2B + C = 28 ⇒ (2)

Wednesday ⇒buy 2 apples, 1 banana, 2 carrots ⇒ for €23

∴ 2A + B + 2C = 23 ⇒ (3)

Using the equations (1), (2) and (3)

A[A/B/C] = [SMon/STue/SWed]

`\left[\begin{array}{ccc}1&1&1\\3&2&1\\2&1&2\end{array}\right] \left[\begin{array}{ccc}A\\B\\C\end{array}\right] =\left[\begin{array}{ccc}15\\28\\23\end{array}\right]`

So, the matrix A =
`\left[\begin{array}{ccc}A11&A12&A13\\A21&A22&A23\\A31&A32&A33\end{array}\right] =\left[\begin{array}{ccc}1&1&1\\3&2&1\\2&1&2\end{array}\right]`

And The vector S =
`\left[\begin{array}{ccc}SMon\\STue\\SWed\end{array}\right] =\left[\begin{array}{ccc}15\\28\\23\end{array}\right]`

Solving the system of equations:

So, A = 3 , B = 7 and C = 5

So, the price of one Apple = €3

The price of one Banana = €7

The price of one Carrot = €5