Question

Q2. Answer this question by hand. Consider the matrix

matrix A =

2	6
6	7

1. Determine the eigenvalues and normalized eigenvectors of A
2. Compare the trace of A to the sum of the eigenvalues of A.
3. Compare the determinant of A to the product of the eigenvalues of A.
4. Find A⁻¹ using elementary row operations. Be sure to indicate the elementary row operation used at each step of your calculation.
5. Apply the formula A-1 = adj(A) = to obtain the inverse of A.

Q3. Consider the matrix A given in question Q2. Use R statistical software to determine the eigenvalues and normalized eigenvectors of A, trace of A, determinant of A, and inverse of A. Also determine the eigenvalues and normalized eigenvectors of A^-1. Your answer should include your R code (annotated with comments) and a hand-written or typed summary of the answers from the R output

Answer 1