College algrebra question about matrixs please help!?

Question

[1 1 1 3100 ]
[0 .01 0.02 32 ]
[0 0 3 3600 ]
its supposed to be one large bracket and from this information it says you can see from the matrix that z =1200 how did they get 1200 from simply looking at this?

Fran receives $249 per year in simple interest from investing $3100. Part is invested at 7%, part at 8% and part at 9%. There is $400 more invested at 9% than at 8%. Find the amount invested at 9%.
thats the problem
the answer is 1200

oh my gosh! thank you so much!

Answer 1

Each row of the matrix contains the coefficients of x, y, and z, followed by the answer.

So the third row shows 0x + 0y + 3z = 3600

So 3z = 3600

divide by 3 and you get z = 1200

That's how they got it.

Answer 2

The first row of the matrix represents the equation x+y+z = 3100, which clearly derives from the problem. The second row of the original would have said [.07 .08 .09 249] and represented .07x + .08y + .09z = 249, and the last row, to represent z - y = 400, would have said [0 -1 1 400].

The matrix you're looking at has been worked on a bit and is 1 step away from row-echelon form, in which row 1 starts with 1, row 2 with 0 1, row 3 with 0 0 1, and so on. Looking at row 3, the [0 0 3 3600] represents the equation 3z = 3600, and it is quite easy to see from that that z = 1200.