Question

Let A be a square matrix, A != I, and suppose there exists a positive integer...

Let A be a square matrix, A != I, and suppose there exists a positive integer m such that Am = I. Calculate det(I + A + A2+ ··· + Am-1).

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A square matrix A is said to be idempotent if A2 = A. Let A be...
A square matrix A is said to be idempotent if A2 = A. Let A be an idempotent matrix. Show that I − A is also idempotent. Show that if A is invertible, then A = I. Show that the only possible eigenvalues of A are 0 and 1.(Hint: Suppose x is an eigenvector with associated eigenvalue λ and then multiply x on the left by A twice.) Let W = col(A). Show that TA(x) = projW x and TI−A(x)...
A square matrix A is said to be idempotent if A2 = A. Let A be...
A square matrix A is said to be idempotent if A2 = A. Let A be an idempotent matrix. Show that I − A is also idempotent. Show that if A is invertible, then A = I. Show that the only possible eigenvalues of A are 0 and 1.(Hint: Suppose x is an eigenvector with associated eigenvalue λ and then multiply x on the left by A twice.) Let W = col(A). Show that TA(x) = projW x and TI−A(x)...
Let n be a positive integer and let U be a finite subset of Mn×n(C) which...
Let n be a positive integer and let U be a finite subset of Mn×n(C) which is closed under multiplication of matrices. Show that there exists a matrix A in U satisfying tr(A) ∈ {1,...,n}
Let A be an n × n matrix and let x be an eigenvector of A...
Let A be an n × n matrix and let x be an eigenvector of A corresponding to the eigenvalue λ . Show that for any positive integer m, x is an eigenvector of Am corresponding to the eigenvalue λ m .
Let A = (A1, A2, A3,.....Ai) be defined as a sequence containing positive and negative integer...
Let A = (A1, A2, A3,.....Ai) be defined as a sequence containing positive and negative integer numbers. A substring is defined as (An, An+1,.....Am) where 1 <= n < m <= i. Now, the weight of the substring is the sum of all its elements. Showing your algorithms and proper working: 1) Does there exist a substring with no weight or zero weight? 2) Please list the substring which contains the maximum weight found in the sequence.
Let A be a 2 × 2 matrix satisfying A^k = 0 for some positive integer...
Let A be a 2 × 2 matrix satisfying A^k = 0 for some positive integer k. Show that A^2 = 0.
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
Let A be a 2x2 matrix and suppose that det(A)=3. For each of the following row...
Let A be a 2x2 matrix and suppose that det(A)=3. For each of the following row operations, determine the value of det(B), where B is the matrix obtained by applying that row operation to A. a) Multiply row 1 by -4 b) Add 4 times row 2 to row 1 c) Interchange rows 2 and 1 Resulting values for det(B): a) det(B) = b) det(B) = c) det(B) =
Let m be a composite positive integer and suppose that m = 4k + 3 for...
Let m be a composite positive integer and suppose that m = 4k + 3 for some integer k. If m = ab for some integers a and b, then a = 4l + 3 for some integer l or b = 4l + 3 for some integer l. 1. Write the set up for a proof by contradiction. 2. Write out a careful proof of the assertion by the method of contradiction.
Let M=[[116,−48],[−48,44]]. Notice that 20 is an eigenvalue of M. Let U be an orthogonal matrix...
Let M=[[116,−48],[−48,44]]. Notice that 20 is an eigenvalue of M. Let U be an orthogonal matrix such that (U^−1)(M)(U) is diagonal, the first column of U has positive entries, and det(U)=1. Find (√20)⋅U.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT