Question

Given A, 2 by 2 matrix as (−4 2 1 −3) find a formula for Ak...

Given A, 2 by 2 matrix as

(−4 2

1 −3)

find a formula for Ak for any positive integer k. the answer should be in the form of a single 2 ×2 matrix.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
find all eigenvalues and eigenvectors of the given matrix A= [3 2 2 1 4 1...
find all eigenvalues and eigenvectors of the given matrix A= [3 2 2 1 4 1 -2 -4 -1]
Given a matrix F = [3 6 7] [0 2 1] [2 3 4]. Use Cramer’s...
Given a matrix F = [3 6 7] [0 2 1] [2 3 4]. Use Cramer’s rule to find the inverse matrix of F. Given a matrix G = [1 2 4] [0 -3 1] [0 0 3]. Use Cramer’s rule to find the inverse matrix of G. Given a matrix H = [3 0 0] [-1 1 0] [-2 3 2]. Use Cramer’s rule to find the inverse matrix of H.
. Given the matrix A = 1 1 3 -2 2 5 4 3 −1 2...
. Given the matrix A = 1 1 3 -2 2 5 4 3 −1 2 1 3 (a) Find a basis for the row space of A (b) Find a basis for the column space of A (c) Find the nullity of A
find the solution to the recurrence relation ak=ak-1+2ak-2+2 with the initial condition a0=4 and a1 =...
find the solution to the recurrence relation ak=ak-1+2ak-2+2 with the initial condition a0=4 and a1 = 12
let's fix a positive integer n. for a nonnegative integer k, let ak be the number...
let's fix a positive integer n. for a nonnegative integer k, let ak be the number of ways to distribute k indistinguishable balls into n distinguishable bins so that an even number of balls are placed in each bin (allowing empty bins). The generating function for sequence ak is given as 1/F(x). Find F(x).
3. a) For any group G and any a∈G, prove that given any k∈Z+, C(a) ⊆...
3. a) For any group G and any a∈G, prove that given any k∈Z+, C(a) ⊆ C(ak). (HINT: You are being asked to show that C(a) is a subset of C(ak). You can prove this by proving that if x ∈ C(a), then x must also be an element of C(ak) for any positive integer k.) b) Is it necessarily true that C(a) = C(ak) for any k ∈ Z+? Either prove or disprove this claim.
Suppose A is a diagonalisable matrix and let k ≥ 1 be an integer. Show that...
Suppose A is a diagonalisable matrix and let k ≥ 1 be an integer. Show that each eigenvector of A is an eigenvector of Ak and conclude that Ak is diagonalisable
#2. For the matrix A =   1 2 1 2 3 7 4 7...
#2. For the matrix A =   1 2 1 2 3 7 4 7 9   find the following. (a) The null space N (A) and a basis for N (A). (b) The range space R(AT ) and a basis for R(AT ) . #3. Consider the vectors −→x =   k − 6 2k 1   and −→y =   2k 3 4  . Find the number k such that the vectors...
Matrix A is given as A = 0 2 −1 −1 3 −1 −2 4 −1...
Matrix A is given as A = 0 2 −1 −1 3 −1 −2 4 −1    a) Find all eigenvalues of A. b) Find a basis for each eigenspace of A. c) Determine whether A is diagonalizable. If it is, find an invertible matrix P and a diagonal matrix D such that D = P^−1AP. Please show all work and steps clearly please so I can follow your logic and learn to solve similar ones myself. I...
For these two problems, use the definition of eigenvalues. (a) An n × n matrix is...
For these two problems, use the definition of eigenvalues. (a) An n × n matrix is said to be nilpotent if Ak = O for some positive integer k. Show that all eigenvalues of a nilpotent matrix are 0. (b) An n × n matrix is said to be idempotent if A2 = A. Show that all eigenvalues of a idempotent matrix are 0, or 1.