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liliy

  • 3 years ago

LINEAR ALGEBRA : Prove that the transformation LA:R^n R^m induced by the m x n matrix A is linear.

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  1. yakeyglee
    • 3 years ago
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    Linear transformations produced by matrices are defined as functions as follows. (here, taking your problem's example of transformation \(LA\)).\[LA(\vec x) = A\vec x\]Here, \(\vec x \in \mathbb R^n\) and \(A\vec x \in \mathbb R^m\), as you specified. Remember, if you want to show that \(f:A\rightarrow B\) is a linear transformation, you need to show that for all \(a_1, a_2 \in A\) and all constants \(C_1, C_2 \in \mathbb R\) that \[f(C_1a_1+C_2a_2)=C_1 f(a_1) + C_2 f(a_2).\]Does this give you enough information to proceed?

  2. liliy
    • 3 years ago
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    wow, i dont really understand i tho. can u say it more in english than math lol

  3. yakeyglee
    • 3 years ago
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    Try reading it slowly.

  4. liliy
    • 3 years ago
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    ouch.

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