Question

Let A and B be n x n matrices and c be a scalar. Prove that,...

Let A and B be n x n matrices and c be a scalar. Prove that, if B is obtained by muliplying a row of A by c, then |B|= c|A|.

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
Let A, B, and C be n×n matrices of the form A= [c_1...x...c_n], B= [c_1...y...c_n], and...
Let A, B, and C be n×n matrices of the form A= [c_1...x...c_n], B= [c_1...y...c_n], and C= [c_1...x+y...c_n] where x, y, and x+y are the jth column vectors. Use cofactor expansions to prove that det(C)=det(A)+det(B).
Let A, B ? Mn×n be invertible matrices. Prove the following statement: Matrix A is similar...
Let A, B ? Mn×n be invertible matrices. Prove the following statement: Matrix A is similar to B if and only if there exist matrices X, Y ? Mn×n so that A = XY and B = Y X.
Let B be an mxn matrix. Prove c is a non-zero scalar, then dim(rowspace(cB)) = dim(rowspace(B)).
Let B be an mxn matrix. Prove c is a non-zero scalar, then dim(rowspace(cB)) = dim(rowspace(B)).
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 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...
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?
Q.Let A and B be n × n matrices such that A = A^2, B =...
Q.Let A and B be n × n matrices such that A = A^2, B = B^2, and AB = BA = 0. (a) Prove that rank(A + B) = rank(A) + rank(B). (b) Prove that rank(A) + rank(In − A) = n.
4.4.3. Suppose A and B are n × n matrices. Prove that, if AB is invertible,...
4.4.3. Suppose A and B are n × n matrices. Prove that, if AB is invertible, then A and B are both invertible. Do not use determinants, since we have not seen them yet. Hint: Use Lemma 4.4.4. Lemma 4.4.4. If A ∈ Mm,n(F) and B ∈ Mn,k(F), then rank(AB) ≤ rank(A) and rank(AB) ≤ rank(B).
Show that the set GLm,n(R) of all mxn matrices with the usual matrix addition and scalar...
Show that the set GLm,n(R) of all mxn matrices with the usual matrix addition and scalar multiplication is a finite dimensional vector space with dim GLm,n(R) = mn. Show that if V and W be finite dimensional vector spaces with dim V = m and dim W = n, B a basis for V and C a basis for W then hom(V,W)-----MatB--->C(-)--------> GLm,n(R) is a bijective linear transformation. Hence or otherwise, obtain dim hom(V,W). Thank you!
3.a) Let n be an integer. Prove that if n is odd, then (n^2) is also...
3.a) Let n be an integer. Prove that if n is odd, then (n^2) is also odd. 3.b) Let x and y be integers. Prove that if x is even and y is divisible by 3, then the product xy is divisible by 6. 3.c) Let a and b be real numbers. Prove that if 0 < b < a, then (a^2) − ab > 0.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT