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title: “matrices” author: “Yadu” date: “July 22, 2015” output: html_document

Problem 1:

A <- matrix(c(1,2,-1, 2,1,1, -3,-3,0), ncol = 3, byrow = TRUE)
b <- matrix(c(5,13,-8), ncol = 1)
require('MASS')

## Loading required package: MASS

giA <- ginv(A)
x <- giA%*%b #computes the cross product of the inverse matrix and the column vector 
x

##           [,1]
## [1,] 3.2222222
## [2,] 0.5555556
## [3,] 2.6666667

Problem 2:

C <- matrix(c(4,-3,-3,5,0,1), ncol = 2, byrow = TRUE)
D <- matrix(c(1,3,4,-2), ncol = 2)
y <- C%*%D
y

##      [,1] [,2]
## [1,]   -5   22
## [2,]   12  -22
## [3,]    3   -2