Module # 5 Doing Math
First, two matrices, A and B, with respective dimensions of 10x10 and 10x100, are defined in the manner that is described. The determinant of matrix A is then computed by the code using the det() function, and its non-zero value indicates whether matrix A is unique or invertible. When matrix A's determinant is zero, showing that it is singular, an alert stating that "Matrix A is singular and doesn't have an inverse" is printed.
Following this, the code tries to print matrix A's inverse, but because of its singularity, the output message is not complete and shows "Inverse of matrix A:" and a blank line. The matrix A determinant is then printed by the code. A message reading "Determinant of matrix B cannot be calculated as it is not a square matrix" is printed because matrix B is not a square matrix, making it impossible to calculate the determinant. All things considered, the process shows how to determine matrix singularity, compute the determinant, and work with non-square matrices in R.
The following output followed, as displayed in the screenshot:
> # Define matrices A and B
> A <- matrix(1:100, nrow = 10)
> B <- matrix(1:1000, nrow = 10)
>
> # Calculate determinant of matrix A
> det_A <- det(A)
>
> # Check if matrix A is invertible
> if (det_A != 0) {
+ # Matrix A is invertible, so calculate its inverse
+ A_inv <- solve(A)
+ } else {
+ # Matrix A is singular and doesn't have an inverse
+ cat("Matrix A is singular and doesn't have an inverse.\n")
+ A_inv <- NULL
+ }
Matrix A is singular and doesn't have an inverse.
>
> # Print results for matrix A
> cat("Inverse of matrix A:\n")
Inverse of matrix A:
> if (!is.null(A_inv)) {
+ print(A_inv)
+ }
> cat("\nDeterminant of matrix A:", det_A, "\n")
Determinant of matrix A: 0
>
> # Print message for matrix B
> cat("\nDeterminant of matrix B cannot be calculated as it is not a square matrix.\n")
Determinant of matrix B cannot be calculated as it is not a square matrix.
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