Use the following parts to find A^(7), where A=[[-6,18],[6,6]]. (a) (1 point) Given the eigenvalues are lambda _(1)=12 and lambda _(2)=-12 with corresponding eigenvectors v_(1)=[[1],[1]] and v_(1)=[[-3],[1]], find the invertible matrix P to diagonalize A, i.e., A=PDP^(-1). P= (b) (1 point) Find P^(-1). P^(-1)= (c) (1 point) Write the diagonal mat

Question

Use the following parts to find A^(7), where A=[[-6,18],[6,6]]. (a) (1 point) Given the eigenvalues are  lambda _(1)=12 and  lambda _(2)=-12 with corresponding eigenvectors v_(1)=[[1],[1]] and v_(1)=[[-3],[1]], find the invertible matrix P to diagonalize A, i.e., A=PDP^(-1). P= (b) (1 point) Find P^(-1). P^(-1)= (c) (1 point) Write the diagonal matrix D. D= (d) (2 points) Derive a general formula involving k for A^(k) using the fact that A=PDP^(-1). Start from A^(2), then A^(3), to generate A^(k). HINT: Only work in variables PDP^(-1) for A^(2) and A^(3). WORK: A^(2)= A^(3)= A^(k)= (e) (2 points) Find A^(7) (Do not multiply A by itself 7 times. This will earn 0 points). A^(7)=

Accepted Answer

Expert Answer to - Use the following parts to find A^(7), where A=[[-6,18],[6,6]]. (a) (1 point) Given the eigenvalues

Answer

Solution for - Use the following parts to find A^(7), where A=[[-6,18],[6,6]]. (a) (1 point) Given the eigenvalues

Answer

This an additional answer to - Use the following parts to find A^(7), where A=[[-6,18],[6,6]]. (a) (1 point) Given the eigenvalues

(Solved): Use the following parts to find A^(7), where A=[[-6,18],[6,6]]. (a) (1 point) Given the eigenvalues ...

View Expert Answer

Expert Answer

Buy This Answer $5

Place Order