Question

Assume all matrices are 3 × 3 prove that if two rows of A are interchanged...

Assume all matrices are 3 × 3 prove that if two rows of A are interchanged to produce B an upper
triangular matrix, then det(A) = − det(B)

Homework Answers

Answer #1

This is the required proof.I hope the answer will help you.Expecting a thumbs up if you are satisfied with the work,it will help me a lot.Thank you.

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
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?
What condition should hold in order to multiply two matrices? A. The number of columns of...
What condition should hold in order to multiply two matrices? A. The number of columns of the first matrix should be equal to the rows of the second matrix. B. The number of rows of the first matrix should be equal to the columns of the second matrix. C. None of the above. D. Two matrices should have the same size.
Prove that any Givens rotator matrix in R2 is a product of two Householder reflector matrices....
Prove that any Givens rotator matrix in R2 is a product of two Householder reflector matrices. Can a Householder reflector matrix be a product of Givens rotator matrices?
In what follows, A and B denote 2 x 2 matrices. Answer each question below, with...
In what follows, A and B denote 2 x 2 matrices. Answer each question below, with justification. No one answer should be more than a few lines long. A1. If k is a scalar, how does the determinant of kA relate to the determinant of A? A2. Show that the determinant of A + B is not necessarily the same as det A + det B. (Remark: a single specific counterexample suffices!) A3. If A is singular and B is...
Prove the following statements: a) If A and B are two positive semidefinite matrices in IR...
Prove the following statements: a) If A and B are two positive semidefinite matrices in IR ^ n × n , then trace (AB) ≥ 0. If, in addition, trace (AB) = 0, then AB = BA =0 b) Let A and B be two (different) n × n real matrices such that R(A) = R(B), where R(·) denotes the range of a matrix. (1) Show that R(A + B) is a subspace of R(A). (2) Is it always true...
Let A and B be 3x3 matrices with det(A) = 2 and det(B) = -3. Find...
Let A and B be 3x3 matrices with det(A) = 2 and det(B) = -3. Find a. det(AB) show all steps. b. det(2B) show all steps. c. det(AB^-1) show all steps. d. det(2AB) show all steps.
prove that type 1 elementary matrix is a product of type 2 and 3 elementary matrices
prove that type 1 elementary matrix is a product of type 2 and 3 elementary matrices
(3 pts) Let A be a square n × n matrix whose rows are orthogonal. Prove...
(3 pts) Let A be a square n × n matrix whose rows are orthogonal. Prove that the columns of A are also orthogonal. Hint: The orthogonality of rows is equivalent to AAT = I ⇒ ATAAT = AT
Given two unitary matrices Q1, Q2 and suppose det(Q1) = -det(Q2). Show that matrix Q =...
Given two unitary matrices Q1, Q2 and suppose det(Q1) = -det(Q2). Show that matrix Q = Q1 + Q2 is singular. hint: consider Q* = Q1*(Q2 + Q1)Q2* and det(Q) .
Let G be the set of all 2x2 matrices [a a a a] such that a...
Let G be the set of all 2x2 matrices [a a a a] such that a is in the reals and a does not equal 0. Prove or disprove that G is a group under matrix multiplication.