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anonymous

  • 5 years ago

Anyone here good with linear algebra?

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  1. anonymous
    • 5 years ago
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    Yes, what's your question?

  2. anonymous
    • 5 years ago
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    Suppose A is an nxn matrix, whose determinant is not equal to zero and which satisfies the following condition: A^2=A. Prove that A must be equal to In, where I is the identity matrix. Cite any theorems/ definitions used. It'd be a great help if I could get a little "push" or hint.

  3. anonymous
    • 5 years ago
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    Are you taking a college course or middle school? If it's a college course, then you're further ahead than I am.

  4. anonymous
    • 5 years ago
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    Sorry, high school*

  5. anonymous
    • 5 years ago
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    Jzzkc, linear algebra isn't the same thing as the algebra of linear equations. :P

  6. anonymous
    • 5 years ago
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    College course :(

  7. anonymous
    • 5 years ago
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    Det =/= 0 <=> There Exists a nxn matrix B s.t AB = I = BA.

  8. anonymous
    • 5 years ago
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    => A^2 = AA = A => AAB = AB => AI = I => A = I

  9. anonymous
    • 5 years ago
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    How did you get A62 = AA to become A?

  10. anonymous
    • 5 years ago
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    A^2 = A. The matrix satisfies this condition.

  11. anonymous
    • 5 years ago
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    and A^2 = AA.

  12. anonymous
    • 5 years ago
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    Are you also famliar with span and null space?

  13. anonymous
    • 5 years ago
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    Yes I suppose so.

  14. anonymous
    • 5 years ago
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    How did you get from the A^2=AA=A step to the step AAB=AB?

  15. anonymous
    • 5 years ago
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    I multiplied B, the matrix that has the property AB = I = AB. The Inverse of A. You could multiply it like this => BAA = BA too if you want.

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