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

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]

So, the matrix A =

And The vector S =

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

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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