Question

5. (a) Prove that det(AAT ) = (det(A))2. (b) Suppose that A is an n×n matrix...

5. (a) Prove that det(AAT ) = (det(A))2.
(b) Suppose that A is an n×n matrix such that AT = −A. (Such an A is called a skew- symmetric matrix.) If n is odd, prove that det(A) = 0.

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
1. If A is an n n matrix, prove that (a) ATA is a symmetric matrix....
1. If A is an n n matrix, prove that (a) ATA is a symmetric matrix. (b) A + AT is a symmetric matrix and A - AT is a skew-symmetric matrix. (c) A is the sum of a symmetric and a skew-symmetric matrix.
If I prove Det(A)Det(B) = Det(AB) for matrices A and B when A and B are...
If I prove Det(A)Det(B) = Det(AB) for matrices A and B when A and B are 2x2 matrices, can I use that to show that Det(A)Det(B) = Det(AB) for any n x n matrix? If so how?
Let A be an n × n-matrix. Show that there exist B, C such that B...
Let A be an n × n-matrix. Show that there exist B, C such that B is symmetric, C is skew-symmetric, and A = B + C. (Recall: C is called skew-symmetric if C + C^T = 0.) Remark: Someone answered this question but I don't know if it's right so please don't copy his solution
Let A be an n×n nonsingular matrix. Denote by adj(A) the adjugate matrix of A. Prove:...
Let A be an n×n nonsingular matrix. Denote by adj(A) the adjugate matrix of A. Prove: 1)   det(adj(A)) = (det(A)) 2)    adj(adj(A)) = (det(A))n−2A
Suppose A, B, C are n x n matrices with det. A =1,det B =-1, det...
Suppose A, B, C are n x n matrices with det. A =1,det B =-1, det C is 2, find AB, A+B,
prove that if E is elementary matrix, then E^T is also elementary matrix and det(E^T)=det(E)
prove that if E is elementary matrix, then E^T is also elementary matrix and det(E^T)=det(E)
n×n-matrix M is symmetric if M = M^t. Matrix M is anti-symmetric if M^t = -M....
n×n-matrix M is symmetric if M = M^t. Matrix M is anti-symmetric if M^t = -M. 1. Show that the diagonal of an anti-symmetric matrix are zero 2. suppose that A,B are symmetric n × n-matrices. Prove that AB is symmetric if AB = BA. 3. Let A be any n×n-matrix. Prove that A+A^t is symmetric and A - A^t antisymmetric. 4. Prove that every n × n-matrix can be written as the sum of a symmetric and anti-symmetric matrix.
Suppose that M is an n×n matrix of finite order. Find all possible values for det(M).
Suppose that M is an n×n matrix of finite order. Find all possible values for det(M).
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) =
A matrix A is symmetric if AT = A and skew-symmetric if AT = -A. Let...
A matrix A is symmetric if AT = A and skew-symmetric if AT = -A. Let Wsym be the set of all symmetric matrices and let Wskew be the set of all skew-symmetric matrices (a) Prove that Wsym is a subspace of Fn×n . Give a basis for Wsym and determine its dimension. (b) Prove that Wskew is a subspace of Fn×n . Give a basis for Wskew and determine its dimension. (c) Prove that F n×n = Wsym ⊕Wskew....
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT