How to Find Bases for Image & Kernel - M502 (S21)

#Linear Algebra

[@rohanjoshi9490]

Thanks mate , it helped a lot , straight to the point and well explained.

[@wishizuk]

Thanks for your kind words! I hope that you will enjoy my other videos!

[@Sky-line81]

Thank you for this. Really needed this. Keep up the good work👏

[@wishizuk]

My pleasure! I am glad to hear that it was helpful. Will do! Thanks for your kind words!

[@ngoco3588]

Thank you so much. It's really helpful for me

[@wishizuk]

Glad to hear!

[@samuelzheng2707]

lets say, there is a single 1 in a column but its a negative, would that still work?

[@wishizuk]

You can simply multiply the row of -1 by -1 to turn it into +1.

[@renatovenegas1313]

so basically for all lineal transformation we work whit the associated matrix of a certain basis?

[@wishizuk]

Yes, every linear transformation between finite vector spaces is associated with a matrix.

[@jujuhybrid3775]

so the basis of the migae can be read of the matrix by looking back at the columns that consisted of just a single 1 and otherwise 0?

[@wishizuk]

Yes, that is correct.

[@garrettroach8160]

Thanks for the help!

[@wishizuk]

My pleasure!

[@berkeklk]

thanks that was helpful

[@wishizuk]

My pleasure!

[@ozimozim2148]

Thank you for this video

[@wishizuk]

My pleasure!

[@mr.austinhailubasinger7822]

So is finding the basis for the image the same as finding a basis for the column space?

[@wishizuk]

Yes, it is since the image is a collection of all linear combinations of column vectors.

[@TheClockmister]

@@wishizuk But you can put the vectors as rows right, or do we by convention always put the vectors as columns

[@sbarisemre]

thanks king

[@wishizuk]

My pleasure!