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• Calcular el null space amb LaTeX, veure exactament els passos intermitjos.
• Ensenyar d'alguna manera que el rowspace i el nullspace són perpendiculars (el mateix per column space i left null space).
• Extendre l'app a matrius rectangulars: 2x3 i 3x2 (potencialment 1x3, 2x1 etc).

• Relació entre el rank i la dimensió del null space: crear un parell de diapositives per separat on es vegi que Ax es pot multiplicar column-wise, i llavors arribem a la noció de vectors linearment independents.
• Quan ensenyo la app, a la visualització hauria de recordar-los-hi que "a linear transformation is completely defined by where the basis vectors land". Això ho puc ensenyar amb els punts del quadrat en el tab "visualization"
• Matriu inversa i dimensió del null space: carregar el video del Gilbert strang o preparar 2 diapos amb els seus missatges.
• Rotació: explicar el unit circle

Preguntes a fer durant la classe:

• Do you think that with this transformation we will obtain an area, a line or the 0 vectors?
• What is the determinant?
• What is the null space?
• Which is the inverse matrix?

"The matrix is invertible because: all column vectors are linearly independent, the determinant is different than 0, and the null space only contains the 0 vector"

"The Gauss-Jordan tab tells us 4 important things: the inverse matrix (if invertible), a basis for the column space, a base for the null space, and the fundamental theorem of linear algebra"

Hello,

I have found a possible bug in the first Shiny App, at the part that does Gauss-Jordan elimination. If I pass the following matrix A as input:

-4 2 0
2 -1 0 = A
0 1 1

The app begins to add to the second column continuously until it breaks without reaching any column echelon form.

I have also noticed that if I try to reload the webpage right after trying to compute this, it load very slowly and I have to wait a while until I can use it again (it may have been a connection issue, but other webpages seemed to be loading normally).

Let me know if I should provide any additional details about the issue.

Thanks!
Eric

see title

When applying Gauss-Jordan in 3D, the first step should read C2 <- ...; but for now it read C1