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
- 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