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Math Help - Quiz Question...... HELP!!!

  1. #1
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    Quiz Question...... HELP!!!

    The question is.....

    Let u be a solution to Ax = b and v be a solution to Ax = 0, where A is an m x n matrix and b is a vector in R^m. Show that u + v is also a solution to Ax = b.

    To be honest, I don't even know where to start. This was a quiz question on a quiz in my linear algebra class. I thought I had gotten it right, or at least mostly correct. But I got no credit for it whats so ever. Please explain how to do this.

    TIA
    John
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by TreeMoney View Post
    The question is.....

    Let u be a solution to Ax = b and v be a solution to Ax = 0, where A is an m x n matrix and b is a vector in R^m. Show that u + v is also a solution to Ax = b.

    To be honest, I don't even know where to start. This was a quiz question on a quiz in my linear algebra class. I thought I had gotten it right, or at least mostly correct. But I got no credit for it whats so ever. Please explain how to do this.

    TIA
    John
    Assume your givens above. Recall that matrix multiplication distributes over matrix/vector addition.

    Let x = u + v
    Then Ax = A(u + v) = Au + Av = b + 0 = b. (Check!)

    -Dan
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