Perhaps someone can explain. I’m having trouble working out how this matrix comes about. I can work it out no problem with a simultaneous equation solving a first and then substituting.
I can see how the top row becomes 1 and 0.2, but I can’t figure out how the bottom row 0 and 1 comes around. I know this is probably a simple thing, but I’m struggling to comprehend how it came about.
Hello @Michael_Gordon
The 1st column of the matrix represents the coefficient of a and the 2nd column of the matrix represents the coefficient of b. So, if you look at the 2nd equation in the intermediate system, there is no “a” term, which means the coefficient of a is 0, while the coefficient of b is 1. Hence the 2nd row of the matrix is 0 and 1
Hi Shanup,
Thanks for the response. I understand the values correspond to the coefficient. The problem I was having was understanding how to reduce the 2nd row. However, I think I have figured it out now.
great catch ! I am stuck too - I tried multiplying with 0.2 with row 2 and subtract with row 1 but it ends up having
1 0
1 1
which is not the answer ! 
I wish the instructor replies to this thread !
I got little bamboozled by that too.
I have done plenty of this in past but got super confused.
My simple guess step wise are:
|5 1|
|4 -3|
R1 → R1/5
|1 0.2|
|4 -3|
R2 → R2 - R1*4
|1 0.2|
|0 -3.8|
R2 → R2/(-3.8) {Divide second row by -3.8}
|1 0.2|
|0 1|
R1 → R1 - R2*0.2
|1 0|
|0 1|
The way instructor did it was little different but not wrong either.
Divided both rows by 5 and 4 respectively, to get:
|1 0.2|
|1 -0.75|
Then subtract second row with first one:
|1 0.2|
|0 -0.95|
And then divide second row with -0.95, and you get:
|1 0.2|
|0 1|
And you can further do the last step as I did in previous way.
Hi Michael_Gordon and all.
You have to solve it using the elimination method by reducing the coefficients of “a” (in row 1) and “b” (in row 2) to 1.
To reduce coefficient of “a”:
In row 1 of the original matrix, divide it by the left-most coefficient of row 1 (in this case, 5), resulting in 1 and 0.2.
In row 2 of the original matrix, divide it by the left-most coefficient of row 2 (in this case, 4), resulting in 1 and -0.75.
To eliminate “a” from row 2:
Subtract row 1 from row 2, so in this case 1 - 1 = 0 and -0.75 - 0.2 = -0.95.
To reduce coefficient of “b”:
Divide row 2 by the current coefficient of “b”, in this case 0 / -0.95 = 0 and -0.95 / -0.95 = 1.
Godspeed!
