G Given the system of equations: 15 c1 – 5 c2 – c3 = 2400 - 5 c1 + 18 c2 – 6 c3 = 3500 - 4 c1 - c2 + 12 c3 = 4000 (a) Calculate the inverse of the matrix? (b) Use the inverse to solve the problem. (c) Determine how much the load in equations 3 needs to be changed by to achieve a 15 % increase in c1.

Answer

(a)

(b)

Step-by-step explanation:

Remember that when you want to solve a problem like this, you express the equation as following

So, if you know the inverse of     then

For this case

Now for this case the inverse of A would be

Then when you multiply with the vector solution

So from that information you can conclude that  the solution to the system of equations is  x = 500/7   y = 2400/7  and z = 2700/7