Linear Alg Prac : S102B

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• Matrix Mult Example

  • https://chatgpt.com/share/69d00838-2770-83e8-ba95-c0ea956b8ef0

A_1 <- matrix(c(1,2,3,4,5,6), nrow=2, byrow=TRUE)
B_1 <- matrix(c(7,8,9,10), nrow=2, byrow=TRUE)

A_2 <- matrix(c(1,2,3,4), nrow=2, byrow=TRUE)
B_2 <- matrix(c(5,6,7,8), nrow=2, byrow=TRUE)

A_3 <- matrix(c(1,0,2,-1,3,1), nrow=2, byrow=TRUE)
B_3 <- matrix(c(2,1,0,1,3,2), nrow=3, byrow=TRUE)

b1 <- c(7,8)
b2 <- c(9,10)

a1 <- c(1,4)
a2 <- c(2,5)
a3 <- c(3,6)

c1 <- c(b1 %*% a1, b1%*%a2, b1%*%a3)
c2 <- c(b2 %*% a1, b2%*%a2, b2%*%a3)
C <- matrix(c1, c2,  nrow= 2, ncol=3)

C

##      [,1] [,2] [,3]
## [1,]   39   54   69
## [2,]   39   54   69

# verify solution : 
B_1 %*% A_1

##      [,1] [,2] [,3]
## [1,]   39   54   69
## [2,]   49   68   87