**Question:**

Your assignment MUST be completed in R. Submissions in Word or…

Your assignment MUST be completed in R. Submissions in Word or Excel will not be accepted. Submit only your R code, with your answers included in the code as a comment (using the # symbol).

Question : Assumes the following matrix

Z=

⎣500 350 110⎤

⎢320 350 20 ⎥

⎡-5 -64 34 ⎦

and the vector of constants

b=

⎣1097 ⎦

⎢453⎥

⎡117⎤

Let us now consider the summation vector i of appropriate dimension, as well as the vector of unknown constants d. What are the values of the vector d if

a) Our equation system is Zi+d=b ?

b) Our equation system is iTZ+dT=bT ?

you have to find the questions using matrix calculation concepts in R

## Solution:- R Matrix and Vector of Constants Assignment

To find the values of the vector `d`

for the equation systems `Zi+d=b`

and `iTZ+dT=bT`

, you can use matrix calculations in R. Here’s the R code to solve both parts of the problem:

# Define the matrix Z and vector b

`Z <- matrix(c(500, 320, -5, 350, 360, -64, 110, 20, 34), nrow = 3, ncol = 3)`

b <- c(1097, 453, 117)

# a) Solve for d in Zi + d = b

`d_a <- solve(Z, b)`

# b) Solve for d in iTZ + dT = bT

`iT <- t(Z) # Transpose of Z`

dT <- t(b) # Transpose of b

d_b <- solve(iT, dT)

# Print the results

`cat("a) Vector d for Zi + d = b:", d_a, "\n")`

cat("b) Vector d for iTZ + dT = bT:", d_b, "\n")

In this code:

The results will be printed, showing the values of the vector `d`

for both equation systems.