Another example of a projection matrix | Linear Algebra | Khan Academy

[@debendragurung3033]

9:50. which matrix is valid this one or the ones with two colu,ns?

[@yonghuiliew8066]

The one in 9:50. he messed up the one with two columns cuz he assumed x2 and x3 to be free variables

[@97021840]

just great

[@debendragurung3033]

the whole projection has me lost

[@yonghuiliew8066]

How do you know if x2 and x3 are free variables to begin with? You can't just assume x2 and x3 to be free variables and let them equal to c. Therefore, your transformation matrix A in the beginning is wrong.

[@legacies9041]

This is just an example @Yong Hui Liew and not a proof! Please pay attention!

[@TürkanBetülDemirtaş]

when you transform them into a matrix, x1 will be the pivot and the others will be free variables

[@MrPeeepe]

Too slow