Question

Matrix help?

Answer 1

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.

Answer 2

Wow!

"If x, y, and z represent the easy, medium, and expert levels, respectively" interpret this to mean that x, y and z represent the COUNT of each the easy, medium and expert levels.

Others here on OS might be more willing to try lending you a hand if you'd please first invest some time and effort into analyzing this problem and sharing your thoughts.

Answer 3

In statements, sentences with "requirements" can be translated into equations. Luckily (it's your chapter's topic), yours can be translated into linear equations. (no powers, no "strange" functions, just constant coefficients and '+' and '-' operations, as in "2x+y-4z=C")

As @mathmale said, give names to the unknowns: write \(x,y,z\) for the number of points of level Easy, Medium, and Hard respectively.

`The total score needed to clear all three difficulty levels is 7,500.` is translated as
\[x+y+z=1500\]

1) How do you translate `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.` ?

2) How do you translate `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.`?

At the end of 1) and 2), adding the previous equation found, you will have 3 equations of 3 unknowns. -> Write everything in matrix form.

Answer 4

\[x+y+z=7500\] <--- typo.. I wrote 1500 :\

Answer 5

2x -500 = y?

Answer 6

For #1

Answer 7

yes

Answer 8

2y -1500 = z

Answer 9

yes again. Now the matrix

Answer 10

That's the hard part for me

Answer 11

Okay. With equations are already written down, it's a mechanical process: an equation's coefficient will be put horizontally in the matrix. But before doing that, you must rewrite all equations in the form \(ax+by+cz=d\). (variables on the left, constant on the right)

Answer 12

You must rewrite the two last equations.

Answer 13

I'll show it for the second one.
\(2x - 500 = y\). That will become \(2x-y = 500\). Now you do the rewriting for the 3rd equation.

Answer 14

2x−y=500

Answer 15

Sorry my computer is being really slow

Answer 16

2y - z = 1500?

Answer 17

yes.

Answer 18

Okay, I think I have it from here. Thank you

Answer 19

yw