How to Find the Rank of a Matrix (with echelon form) | Linear Algebra

The rank of a matrix is the number of linearly independent rows or the number of linearly independent columns the matrix has. These definitions are equivalent. To find this number, we can reduce a matrix to row echelon form and count the nonzero rows, whose leading entries are called pivot numbers. We'll solve five rank of a matrix examples in this lesson. #linearalgebra

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[nomyamar]

As someone struggling with university math, this was super helpful. Thank you so much.

[kacpersambor]

finally someone who managed to clearly explain what to do, thanks a lot

[Batooya]

I love how simple you made this explanation to be. My professor basically lectures like we've taken the course before and it's been kinda rough.

[fireheart]

This was the simplest and clearest explanation I have ever heard of rank, no complicated concepts, no silly jumps from one matrix to another. Thank you so much for such a clear explanation :)

[heacac]

at 1:57 what did i miss, ist 2+3 = 5 and C3 ist 4 in its 2nd column ?

[DP-rqnh]

Great video! I had a little trouble following the "row echelon form" examples though. Is this knowledge assumed or explained in a related video? Sorry if I missed it! Still one of the best "rank" videos I've come across!

[jacksongraham]

Your videos are incredible. So well explained and to the point, thank you so much!!!

[yondabigman]

quick, easy to understand, good job!

[ParvejBiswas-qire]

Your 1 minute video is better than others 10 minutes video

[archerdev]

Thank you so much for this great video. Math bless you man

[onlysheriffdeen]

This was super helpful. Thank you so much!

[nihaarsatsangi]

Your content is always presented with such clarity, and I truly appreciate that!! Thanks a lot!
Small verification required: We will calculate the row echelon form when rows and columns in the matrix are linearly independent, right? and then find its
because we did not calculated row echelon form in case of linearly dependent rows and columns ie; matrix C and D

[BrushBurnerBRR]

this is so fkin easy and i hate my maths prof

[thihongngale]

The last example still confuses me, the third result in the E matrix, can I add row 4 to row 2 and then add row 2 to row 4 to eliminate them all ? After that I swap row 4 and row 2 so that the rank will equal to 2.

[VedantDarsan-pztn]

Thank you so much 😢 you have cleared the pain of my college math

[Kenn-vdev]

Can simultaneous operations include the same rows? In the last example, where you took R2 - R4 and R4 - R2, when you take R2 - R4, there would be a new R2. However over here, you are taking R4 - old R2

[Furkan-yvew]

Does swithcing from row operations to collumn operations change the result of the rank? Are we looking for row echelon form matrix that is equivaluent to the given matrix?

[mattshort]

I thought that that in row echelon form, all leading entries from the left need to be 1. This seems to contradict example A. Is what have I been told wrong?

[PunmasterSTP]

The "rank" of this video is pretty high 👍