Module 5: Determinant and Inverse of Matrices in R

 This assignment practiced creating matrices in R and computing a determinant and inverse (when possible).

 

Step 1: Creating Matrices A and B 

I created the matrices using matrix(): 

 


Matrix A contains the numbers 1 to 100 arranged into 10 rows.
Matrix B contains the numbers 1 to 1000 arranged into 10 rows.

 

 Step 2: Checking the Dimensions

To check the size of each matrix, I used:


Step 3: Finding the Determinant of A

I used the det() function to find the determinant of A:

This result shows that matrix A is singular, which means it does not have an inverse. 

 

Step 4: Finding the Inverse of A

I attempted to find the inverse of A using:

 

Result:
R returned an error saying that the system is computationally singular.

This confirms that A does not have an inverse because its determinant is zero.

 

Step 5: Testing Matrix B

Since B is not a square matrix, I tested:

 

 

Result:
Both commands returned errors.

This happens because determinants and inverses are only defined for square matrices.

  

Conclusion

From this assignment, I learned that a matrix must be square and have a non-zero determinant in order to have an inverse. Even though matrix A is square, it does not have an inverse because its determinant is zero. Matrix B does not have a determinant or inverse because it is not square. This exercise helped me understand the conditions needed for matrix inversion in R.

 

 

 

 

 

 

 

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