### Problem Set 1

$\left[\begin{array} {rrr} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{array}\right] * \left[\begin{array} {rrr} 1 & 4 & 7 \\ 2 & 5 & 8 \\ 3 & 6 & 9 \end{array}\right] =$

##      [,1] [,2] [,3]
## [1,]   14   32   50
## [2,]   32   77  122
## [3,]   50  122  194

$\left[\begin{array} {rrr} 1 & 4 & 7 \\ 2 & 5 & 8 \\ 3 & 6 & 9 \end{array}\right] * \left[\begin{array} {rrr} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{array}\right] =$

##      [,1] [,2] [,3]
## [1,]   66   78   90
## [2,]   78   93  108
## [3,]   90  108  126
##       [,1]  [,2]  [,3]
## [1,] FALSE FALSE FALSE
## [2,] FALSE FALSE FALSE
## [3,] FALSE FALSE FALSE
1. An identity matrix when transposed and multiplied to itself, are equal to each other
##      [,1] [,2]
## [1,] TRUE TRUE
## [2,] TRUE TRUE

### Problem Set 2

Demonstrations

## [[1]]
## [[1]][[1]]
##      [,1] [,2] [,3]
## [1,]    1    0    0
## [2,]    2    1    0
## [3,]    3    2    1
##
## [[1]][[2]]
##      [,1] [,2] [,3]
## [1,]    1    4    7
## [2,]    0   -3   -6
## [3,]    0    0    0
##
##
## [[2]]
## [[2]][[1]]
##          [,1]      [,2] [,3]
## [1,] 1.000000 0.0000000    0
## [2,] 2.106383 1.0000000    0
## [3,] 1.680851 0.3326171    1
##
## [[2]][[2]]
##               [,1]      [,2]       [,3]
## [1,]  4.700000e+01  66.00000   77.00000
## [2,]  1.421085e-14 -99.02128 -105.19149
## [3,] -4.726773e-15   0.00000  -25.43704
##      [,1] [,2] [,3]
## [1,] TRUE TRUE TRUE
## [2,] TRUE TRUE TRUE
## [3,] TRUE TRUE TRUE
##      [,1] [,2] [,3]
## [1,] TRUE TRUE TRUE
## [2,] TRUE TRUE TRUE
## [3,] TRUE TRUE TRUE