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Math Help - Proofs Help - Matrices

  1. #1
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    Proofs Help - Matrices

    I need some help proving the Matrix Addition in general is associative. Any help is apriciated. Thank you
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by holmesb View Post
    I need some help proving the Matrix Addition in general is associative. Any help is apriciated. Thank you
    Let A B and C be NxM matrices and X_{i,j} denote the i,j th elements of a matrix C. As the i j th component of the sum of two matrices is the sum
    of their individual i j th components and ordinary addition is associative:

    Then [(A+B)+C]_{i,j} = (A+B)_{i,j} + C_{i,j} = A_{i,j} + B_{i,j} + C_{i,j}

    .............................= A_{i,j} + (B+C)_{i,j} = [A+(B+C)]_{i,j}

    RonL
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  3. #3
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    Hello, holmesb!

    Prove that Matrix Addition is associative.

    To add two similar matrices, we add the corresponding elements and create a third matrix.
    . . Symbolically, this can be wirrten: .P + Q .= .(p
    ij) + (qij) .= .(pij + qij)


    Given three similar matrices: .A, B, C
    . . we want to show that: .A + (B + C) .= .(A + B) + C

    Then: .A + (B + C) .= .(a
    ij + [bij + cij]) .[1]

    .and: .(A + B) + C .= .([a
    ij + bij] + cij) .[2]


    Since addition is associative, [1] = [2].

    . . Therefore: .A + (B + C) .= .(A + B) + C

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  4. #4
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    Re:

    Thankyou both for your help.
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