Module # 5 Doing Math

 

Matrix Operations in R: Determinant and Inverse

The goal of this assignment is to learn how to work with matrices in R, specifically how to compute the determinant and inverse of a matrix using built-in R functions.

Step 1: Creating the Matrices

First, I created the two matrices provided in the assignment using the matrix() function.

A <- matrix(1:100, nrow = 10)
B <- matrix(1:1000, nrow = 10)

To better understand these matrices, I checked their dimensions:

dim(A)
dim(B)

  • Matrix A has dimensions 10 × 10, so it is a square matrix.

  • Matrix B has dimensions 10 × 100, so it is not square.

Step 2: Determinant of Matrix A

Since matrix A is square, its determinant can be calculated using the det() function.

det(A)

Result:

The determinant of matrix A is:

0

A determinant of 0 means that matrix A is singular, which has important consequences for finding its inverse.

Step 3: Inverse of Matrix A

The inverse of a matrix in R is calculated using the solve() function.

solve(A)

Result:

R returns an error indicating that the system is computationally singular.

Explanation:

A matrix with a determinant equal to 0 does not have an inverse. Therefore, matrix A cannot be inverted.

Step 4: Determinant and Inverse of Matrix B

Matrix B is not square (10 × 100), so:

  • A determinant is not defined

  • An inverse is not defined

Attempting either operation in R results in an error, which confirms the mathematical rule that only square matrices can have determinants and inverses.

Conclusion

  • Matrix A is square, but its determinant is 0, so it does not have an inverse.

  • Matrix B is not square, so neither a determinant nor an inverse exists.

  • R correctly enforces the rules of matrix algebra when performing these operations.

This assignment helped reinforce the importance of matrix dimensions and determinants when working with inverse matrices in R.

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