# The link between matrix and equation solution

I see we can use row operations to reduce the matrix and reach a “solved system” or the reduced row echelon form of the matrix,

how does that give the solution to the original equations? what are the correct values for the variables?

Hi Basma, which video/assignment are you referring to?

I’m referring to the week 2 conclusion video

you can now comfortably solve systems of equations by translating into matrices and conducting row operations to find a solution in a simple yet fast way.

Hey @Basma_Alkerm,
Please note that when you reduce a matrix into “Row Echelon Form”, or “Reduced Row Echelon Form”, the operations that we use, for instance, adding 2 rows, multiplying a row by a scalar, etc, are applied as is, to the vector of scalars as well, or to be more precise, the matrix of scalars.

In other words, we pose the problem like this, `HX = Y`, where `H` is the matrix of coefficients of the variables (if we have `n` variables, and `n` equations, the matrix will have a dimensionality of `n x n`), `X` is the matrix of variables (dimensionality `n x 1`), and `Y` is the matrix of scalars (dimensionality `n x 1`).

So, whatever operations we apply on `H` to convert it into RREF, we apply the same operations on `Y`, and once we reach the RREF, we just need to find the values one-by-one. I hope that it makes sense now.

Also, you have raised a huge discrepancy as I can see. Although the lecture videos explained REF and RREF in a great detail, they didn’t tell us anything about how to use them to get the solutions for a system of linear equations, (for instance, using an example). I will pass this onto the team to get it fixed.

Cheers,
Elemento

perfectly make sense now

it also can be understood from the programming assignment (I just start it after posting the question), as it stacks the scalers to coefficients before starting the reduction.

i had the same confusion. thank for explaining. Still i do not understand how he got from upper diagonal matrix to diagonal matrix in the video minute 1:32.

Hey @Hassan_Mohamed6,
Apologies for the delayed response. Can you please tell us the lecture video to which you are referring? Basma was referring to the Conclusion video, but I guess you aren’t referring to that one, since the video itself is of 1 min.

Cheers,
Elemento

I found the answer in one of responses. The instructor forgot to add the prices as column to the matrix. In the lab it is shown clearly. There is a gap in the lesson video

Hey @Hassan_Mohamed6,
Can I please request you to point out the lecture video, the time-stamp and the context where you have found the gap? This would help us to correct the discrepancy, and as a result, the future learners won’t face the same issue.

Cheers,
Elemento