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anonymous

  • 5 years ago

(a 1 2) (0 a 1) (1 a 0) That's a matrix. For what values of a is the matrix invertible?

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  1. anonymous
    • 5 years ago
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    This matrix is invertible if and only if the determinate is equal to 0. det=a(a*0-1*a)-0(1*0-2*a)+1(1*1-2*a) 0=a(-a)-0(-2a)+1(1-2a) 0=-a^2+1-2a 0=a^2+2a-1 Using quadratic formula a=-1-sqrt(2) and a=-1+sqrt(2)

  2. anonymous
    • 5 years ago
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    wow. you are smart. thank you

  3. anonymous
    • 5 years ago
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    wait a second - isn't it the other way round? i.e. a matrix is invertible when the determinant is not zero.

  4. anonymous
    • 5 years ago
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    You are correct, I read it wrong. So that means the matrix is invertible for all values except for the ones listed above. If there exists a matrix B such that \[AB=BA=I \] I was supposed to write This matrix is not invertible if and only if the determinate is equal to 0. Nice work :D

  5. anonymous
    • 5 years ago
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    thanks again

  6. anonymous
    • 5 years ago
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    Thank you!

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