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Math Help - Help need

  1. #1
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    Help need

    Hi can someone please help me the following proofs. Look at the picture. Thanks i really appriate it
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by maths_123 View Post
    Hi can someone please help me the following proofs. Look at the picture. Thanks i really appriate it
    For (i) put B=-A.

    For (ii) consider A^{-1}(\alpha A)

    For (iii) consider A^{-1}(AB)=A^{-1}(AC)

    For (v) (vi) and (vii) think about the definition of determinants in terms of sums of products of elements with signs depending on which elements appear in the product.

    CB
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  3. #3
    Junior Member
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    We know that
    det[kA]=k^n *det[A] ...........for nxn matrix A

    (v) is false
    for 2x2 marix A
    det[-A]=(-1)^2 det[A]
    det[-A]= det[A]

    (vi) is true
    for 3x3 martix A
    det[-A]=(-1)^3 *det[A]
    det[-A]=- det[A]

    (vii) is false
    for 3x3 martix A
    det[αA]=α^3 *det[A]
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