Module # 5 Doing Math

Github link: https://github.com/rayhankhan-svg/r-programming-assignments

R Code:

# Create matrices

A <- matrix(1:100, nrow=10)

B <- matrix(1:1000, nrow=10)


# Check dimensions

dim(A)

dim(B)


# Determinants

detA <- det(A)

detA


# Inverses

invA <- tryCatch(solve(A), error=function(e) e)

invB <- tryCatch(solve(B), error=function(e) e)


invA

invB


# Determinant of B

detB <- tryCatch(det(B), error=function(e) e)

detB


Output: 

> # Create matrices
> A <- matrix(1:100, nrow=10)
> B <- matrix(1:1000, nrow=10)
> 
> # Check dimensions
> dim(A)
[1] 10 10
> dim(B)
[1]  10 100
> 
> # Determinants
> detA <- det(A)
> detA
[1] 0
> 
> # Inverses
> invA <- tryCatch(solve(A), error=function(e) e)
> invB <- tryCatch(solve(B), error=function(e) e)
> 
> invA
<simpleError in solve.default(A): Lapack routine dgesv: system is exactly singular: U[3,3] = 0>
> invB
<simpleError in solve.default(B): 'a' (10 x 100) must be square>
> 
> # Determinant of B
> detB <- tryCatch(det(B), error=function(e) e)
> detB
<simpleError in determinant.matrix(x, logarithm = TRUE, ...): 'x' must be a square matrix>
> 


Explanation: 

I made two matrices in R for Module #5:
A <- matrix(1:100, nrow=10) and B <- matrix(1:1000, nrow=10).
I verified that A and B are 10x10 square and 10x100 non-square matrices, respectively, using dim(). I then used det(A) to determine the determinant of A. The outcome was zero, indicating that A is a singular matrix without an inverse. R gave me an error stating that the matrix is singular (not invertible) when I tried to compute the inverse using solve(A). Since determinants and inverses are only defined for square matrices, det(B) and solve(B) failed for matrix B since B is not square.

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