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Math Help - Question about Linear Algebra

  1. #1
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    Unhappy Question about Linear Algebra

    Suppose v1, v2, v3 is a basis for R3 and that A is a 3x3 matrix.

    a. Show that {Av1,Av2,Av3} is linearly independent.

    b. Show that if b is any vector in R3 then span (Av1,Av2,Av3) contains b.

    c. What is it that we just proved in the above exercises?




    I don't even know where to begin I appreciate any help!
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  2. #2
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    Quote Originally Posted by nicolem1051 View Post
    Suppose v1, v2, v3 is a basis for R3 and that A is a 3x3 matrix.

    a. Show that {Av1,Av2,Av3} is linearly independent.


    This is false without one very special condition on the matrix A; for example, take A to be the zero matrix.


    b. Show that if b is any vector in R3 then span (Av1,Av2,Av3) contains b.

    As above

    Tonio

    c. What is it that we just proved in the above exercises?





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