Linear Algebra

posted by .

V = Mnxn is a space vector formed by all the square matrices.

Is W = {A in Mnxn : A^x = A} a subspace of V?


Thanks

  • Linear Algebra -

    No, because if A is in W, then

    B = lambda A

    is not in W if lambda is not equal to 1:

    A^x = A --->

    B^x = lambda^x A^x = lambda^x A =

    labda^(x-1) B

    which is not equal to B for general lambda.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Algebra

    How would you prove this theorem: The column space of an m x n matrix A is a subspace of R^m by using this definition: A subspace of a vector space V is a subset H of V that has three properties: a) the zero vector of V is in H. b) …
  2. linear algebra

    Show that a subset W of a vector space V is a subspace of V if and only if the following condition holds: If u and v are any vectors in W and a and b are any scalars, then au + bv is in W.
  3. math

    Find an orthonormal basis for the subspace of R^3 consisting of all vectors(a, b, c) such that a+b+c = 0. The subspace is two-dimensional, so you can solve the problem by finding one vector that satisfies the equation and then by constructing …
  4. Linear Algebra, orthogonal

    The vector v lies in the subspace of R^3 and is spanned by the set B = {u1, u2}. Making use of the fact that the set B is orthogonal, express v in terms of B where, v = 1 -2 -13 B = 1 1 2 , 1 3 -1 v is a matrix and B is a set of 2 …
  5. Linear Algebra

    1/ Prove that the set V=R+ ( the set of all positive real numbers) is a vector space with the following nonstandard operations: for any x,y belong to R+ & for any scalar c belong to R: x O+ ( +signal into circle) y=x.y (definition …
  6. Linear Algebra

    Find the basis for the following vector space. Please state the dimension of the vector space. S consists of all x in R3 such that x is orthogonal to n=(2,3,2)
  7. Math Elementary Linear Algebra

    determine whether or not the given set forms a basis for the indicated subspace: #1 {1,1,0), (1,1,1)} for the subspace of R^3 of all (x,y,z) such that y= x+z #2 {[1,2,-1,3), (0,0,0,0)} for the subspace of R^4 of all vectors of the …
  8. math

    Which of the following subsets of the vector space Mnn are subspaces?
  9. algebra

    prove that if U and W are vector subspaces of a vector V, then UV, is a vector subspace of V
  10. Math

    Let V and W be vector spaces and assume that T be a linear mapping from V to W. (a) Show that ker(T) is a subspace of V . (b) Show that range(T) is a subspace of W.

More Similar Questions