Question

If A, B and C= A.B are square n×n matrices and the Nullity(C)= 0, then the...

If A, B and C= A.B are square n×n matrices and the Nullity(C)= 0, then the columns of each of these 3 matrices span the same vector space
.

Please give a simple answe thanks

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
Find the dimension of each of the following vector spaces. a.) The space of all n...
Find the dimension of each of the following vector spaces. a.) The space of all n x n upper triangular matrices A with zeros in the main diagonal. b.) The space of all n x n symmetric matrices A. c.) The space of all n x n matrices A with zeros in the first and last columns.
We say two n × n matrices A and B are similar if there is an...
We say two n × n matrices A and B are similar if there is an invertible n × n matrix P such that A = PBP^ -1. a) Show that if A and B are similar n × n matrices, then they must have the same determinant. b) Show that if A and B are similar n × n matrices, then they must have the same eigenvalues. c) Give an example to show that A and B can be...
Given that A and B are n × n matrices and T is a linear transformation....
Given that A and B are n × n matrices and T is a linear transformation. Determine which of the following is FALSE. (a) If AB is not invertible, then either A or B is not invertible. (b) If Au = Av and u and v are 2 distinct vectors, then A is not invertible. (c) If A or B is not invertible, then AB is not invertible. (d) If T is invertible and T(u) = T(v), then u =...
What is the highest possible dimension of a subspace of M_n (R) (set of n×n matrices...
What is the highest possible dimension of a subspace of M_n (R) (set of n×n matrices with real coefficients with its usual vector space structure) that only contains invertible matrices (and 0) ?
Let Mn be the vector space of all n × n matrices with real entries. Let...
Let Mn be the vector space of all n × n matrices with real entries. Let W = {A ∈ M3 : trace(A) = 0}, U = {B ∈ Mn : B = B t } Verify U, W are subspaces . Find a basis for W and U and compute dim(W) and dim(U).
For each of the following statement, determine it is “always true” or “always false”. Explain your...
For each of the following statement, determine it is “always true” or “always false”. Explain your answer. (a) For any matrix A, the matrices A and −A have the same row space. (b) For any matrix A, the matrices A and −A have the same null space. (c) For any matrix A, if A has nullity 0, then A is nonsingular.
Indicate whether each statement is True or False. Briefly justify your answers. Please answer all of...
Indicate whether each statement is True or False. Briefly justify your answers. Please answer all of questions briefly (a) In a vector space, if c⊙⃗u =⃗0, then c= 0. (b) Suppose that A and B are square matrices and that AB is a non-zero diagonal matrix. Then A is non-singular. (c) The set of all 3 × 3 matrices A with zero trace (T r(A) = 0) is a vector space under the usual matrix operations of addition and scalar...
A and B are order-n square matrices, which of the following equations is valid? Select one:...
A and B are order-n square matrices, which of the following equations is valid? Select one: A. (AB)^T=A^TB^T B. A^2−AB^2=(A−B)A C. A^2−B^2=(A+B)(A−B) D. |A^2|=|A|^2
Answer all of the questions true or false: 1. a) If one row in an echelon...
Answer all of the questions true or false: 1. a) If one row in an echelon form for an augmented matrix is [0 0 5 0 0] b) A vector b is a linear combination of the columns of a matrix A if and only if the equation Ax=b has at least one solution. c) The solution set of b is the set of all vectors of the form u = + p + vh where vh is any solution...
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|.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT