Results 1 to 3 of 3

Math Help - subspace and basis (true false)

  1. #1
    Member
    Joined
    Oct 2010
    Posts
    127

    subspace and basis (true false)

    Determine whether the following two are true or false. If true, explain why. If false, give a counter example.

    1. Let A be and m x n matrix and let R = rref(A). Then if S = {v_1,....v_2} is a basis for N(R), then S is a basis for N(A).

    2. If {v_1, v_2, v_3} is a basis for a subspace V of Rn, then {2v_1-2v_2, v_1+v_2+2v_3, v_1+v_3} is also a basis for V.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by Taurus3 View Post
    Determine whether the following two are true or false. If true, explain why. If false, give a counter example.

    1. Let A be and m x n matrix and let R = rref(A). Then if S = {v_1,....v_2} is a basis for N(R), then S is a basis for N(A).

    2. If {v_1, v_2, v_3} is a basis for a subspace V of Rn, then {2v_1-2v_2, v_1+v_2+2v_3, v_1+v_3} is also a basis for V.

    1) What have you done so far?, and

    2) What in the world is "rref"?

    Tonio
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Nov 2010
    From
    Staten Island, NY
    Posts
    451
    Thanks
    2
    I'm guessing that rref(A) is the reduced echelon form of A.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 7
    Last Post: October 5th 2011, 01:45 PM
  2. Replies: 1
    Last Post: October 4th 2011, 03:19 AM
  3. how come false AND false is true?
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: September 24th 2010, 08:41 AM
  4. True or False. Prove if true show counter example if false.
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: March 2nd 2010, 11:54 AM
  5. true/false
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 12th 2009, 09:50 AM

Search Tags


/mathhelpforum @mathhelpforum