Question

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

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
If A is a non singular n × n matrix show that: a) adj(A) is non...
If A is a non singular n × n matrix show that: a) adj(A) is non singular b) [adj(A)]^−1 = det(A^−1 )A = adj(A^−1 )
Let A be an n×n matrix. If there exists k > n such that A^k =0,then...
Let A be an n×n matrix. If there exists k > n such that A^k =0,then (a) prove that In − A is nonsingular, where In is the n × n identity matrix; (b) show that there exists r ≤ n such that A^r= 0.
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.
Prove that if A is a nonsingular nxn matrix, then so is cA for every nonzero...
Prove that if A is a nonsingular nxn matrix, then so is cA for every nonzero real number c.
Show that for each nonsingular n x n matrix A there exists a permutation matrix P...
Show that for each nonsingular n x n matrix A there exists a permutation matrix P such that P A has an LR decomposition. [note: A factorization of a matrix A into a product A=LR of a lower (left) triangular matrix L and an upper (right) triangular matrix R is called an LR decomposition of A.]
Let A be a (n × n) matrix. Show that A and AT have the same...
Let A be a (n × n) matrix. Show that A and AT have the same characteristic polynomials (and therefore the same eigenvalues). Hint: For any (n×n) matrix B, we have det(BT) = det(B). Remark: Note that, however, it is generally not the case that A and AT have the same eigenvectors!
1.Let A be an n x n matrix. Which of these conditions show that A is...
1.Let A be an n x n matrix. Which of these conditions show that A is invertible? •det A= 0 • dim (NulA) = 1 •ColA=R^n •A^T is invertible •an n x n matrix, D, exists where AD=In
Let A be an n by n matrix. Prove that if the linear transformation L_A from...
Let A be an n by n matrix. Prove that if the linear transformation L_A from F^n to F^n defined by L_A(v)=Av is invertible then A is invertible.
3. Let N denote the nonnegative integers, and Z denote the integers. Define the function g...
3. Let N denote the nonnegative integers, and Z denote the integers. Define the function g : N→Z defined by g(k) = k/2 for even k and g(k) = −(k + 1)/2 for odd k. Prove that g is a bijection. (a) Prove that g is a function. (b) Prove that g is an injection . (c) Prove that g is a surjection.
For the matrix A, find (if possible) a nonsingular matrix P such that P−1AP is diagonal....
For the matrix A, find (if possible) a nonsingular matrix P such that P−1AP is diagonal. (If not possible, enter IMPOSSIBLE.) A = 6 −3 −2 1 . Verify that P−1AP is a diagonal matrix with the eigenvalues on the main diagonal.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT