Problem set 1

(1)Show that ATA=AAT (A T A ≠ A A T ) in general. (Proof and demonstration.)

\[ A^TA = AA^T \]

#let's see a 2x2 matrix


 A <- matrix(c(1,-1,2,-2), nrow = 2, byrow = TRUE)
 A
##      [,1] [,2]
## [1,]    1   -1
## [2,]    2   -2
#let's find the tranpose of A, we called it A1
 A1 <- t(A)
 A1
##      [,1] [,2]
## [1,]    1    2
## [2,]   -1   -2
# So we want to demonstrate that A1A =

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