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Math Help - Image of a transformation

  1. #1
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    Image of a transformation

    Describe the image of the transformation T(vector x) = A(vector x) geometrically (line, plane in R^2 or R^3)

    ; means a new row

    A = [2 1 3 ; 3 4 2 ; 6 5 7]. I multiplied this matrix by the [x1 ; x2; x3]. I got x1[2 ; 3 ; 6] + x2[1 ; 4 ; 5] + x3[3 ; 2 ; 7]. Where do I go from here? I'm thinking it's a plane in R^3 but I don't know for sure.

    Thanks
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  2. #2
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    Quote Originally Posted by noles2188 View Post
    Describe the image of the transformation T(vector x) = A(vector x) geometrically (line, plane in R^2 or R^3)

    ; means a new row

    A = [2 1 3 ; 3 4 2 ; 6 5 7]. I multiplied this matrix by the [x1 ; x2; x3]. I got x1[2 ; 3 ; 6] + x2[1 ; 4 ; 5] + x3[3 ; 2 ; 7]. Where do I go from here? I'm thinking it's a plane in R^3 but I don't know for sure.

    Thanks
    reduce A to echelon form or note that 2v_1 - v_2=v_3, where v_j is the j-th column of A. thus the rank of A is 2 and therefore the image is a plane spanned by v_1,v_2.
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