Last updated: 2019-01-25
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| File | Version | Author | Date | Message |
|---|---|---|---|---|
| Rmd | 7bbe37c | John Blischak | 2019-01-25 | Add matrix addition and scalar multiplication. |
\[ A = \begin{bmatrix} -3 & -3 & 3 \\ 1 & 0 & 2 \\ 0 & -2 & 3 \end{bmatrix} \]
\[ B = \begin{bmatrix} -1 & 3 & 3 \\ -2 & 5 & 2 \\ 1 & 2 & 4 \end{bmatrix} \]
\[ C = \begin{bmatrix} -5 & 3 & 9 \\ -3 & 10 & 6 \\ 2 & 2 & 11 \end{bmatrix} \]
In R:
A <- matrix(c(-3, -3, 3,
1, 0, 2,
0, -2, 3),
nrow = 3, byrow = TRUE)
B <- matrix(c(-1, 3, 3,
-2, 5, 2,
1, 2, 4),
nrow = 3, byrow = TRUE)
C <- matrix(c(-5, 3, 9,
-3, 10, 6,
2, 2, 11),
nrow = 3, byrow = TRUE)Find \((A - B) + C\):
(A - B) + C [,1] [,2] [,3]
[1,] -7 -3 9
[2,] 0 5 6
[3,] 1 -2 10Find \(2A + B\):
2 * A + B [,1] [,2] [,3]
[1,] -7 -3 9
[2,] 0 5 6
[3,] 1 -2 10They are equal, therefore:
\[ 2A + B = (A - B) + C \]
\[ A + 2B -C = 0\]
A + 2 * B - C [,1] [,2] [,3]
[1,] 0 0 0
[2,] 0 0 0
[3,] 0 0 0
sessionInfo()R version 3.5.2 (2018-12-20)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Ubuntu 18.04.1 LTS
Matrix products: default
BLAS: /usr/lib/x86_64-linux-gnu/atlas/libblas.so.3.10.3
LAPACK: /usr/lib/x86_64-linux-gnu/atlas/liblapack.so.3.10.3
locale:
[1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
[3] LC_TIME=en_US.UTF-8 LC_COLLATE=en_US.UTF-8
[5] LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8
[7] LC_PAPER=en_US.UTF-8 LC_NAME=C
[9] LC_ADDRESS=C LC_TELEPHONE=C
[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
attached base packages:
[1] stats graphics grDevices utils datasets methods base
loaded via a namespace (and not attached):
[1] workflowr_1.1.1.9001 Rcpp_1.0.0 digest_0.6.18
[4] rprojroot_1.2 backports_1.1.3 git2r_0.24.0
[7] magrittr_1.5 evaluate_0.12 stringi_1.2.4
[10] fs_1.2.6 whisker_0.3-2 rmarkdown_1.11
[13] tools_3.5.2 stringr_1.3.1 glue_1.3.0
[16] xfun_0.4 yaml_2.2.0 compiler_3.5.2
[19] htmltools_0.3.6 knitr_1.21