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monroe17

  • one year ago

If A= x 3 y 3 (matrix) determine the values of x and y for which A^2=A

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  1. satellite73
    • one year ago
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    did you square it?

  2. monroe17
    • one year ago
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    like 3^2?

  3. satellite73
    • one year ago
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    i mean square the matrix

  4. satellite73
    • one year ago
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    i got \[\left[ \begin{array}{ c c } x^2+3y & 3x+9 \\ xy+3y & 3y+9 \end{array} \right]\]

  5. satellite73
    • one year ago
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    assuming the matrix is \[\left[ \begin{array}{ c c } x & 3 \\ y & 3 \end{array} \right]\]

  6. satellite73
    • one year ago
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    that means \[3x+9=3\] so \[x=-2\] and also \(y=-2\)

  7. monroe17
    • one year ago
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    once you square the matrix, how do you determine the x and y values though?

  8. monroe17
    • one year ago
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    oh nevermind. how'd you get 3x+9=3

  9. satellite73
    • one year ago
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    you have \[\left[ \begin{array}{ c c } x^2+3y & 3x+9 \\ x^2+3y & 3y+9 \end{array} \right]=\left[ \begin{array}{ c c } x & 3 \\ y& 3 \end{array} \right]\]

  10. satellite73
    • one year ago
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    assuming my squaring is correct

  11. satellite73
    • one year ago
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    so that means each entry has to be the same for the matrices to be equal

  12. satellite73
    • one year ago
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    therefore \(3x+9=3\implies x=-2\) and \(3y+3=3\implies y=-2\) and so the matrix must be \[\left[ \begin{array}{ c c } -2 & 3 \\ -2 & 3 \end{array} \right]\] by substituting back

  13. satellite73
    • one year ago
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    sorry i meant \(3y+9=3\implies x=-2\)

  14. monroe17
    • one year ago
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    ohhh okay!

  15. satellite73
    • one year ago
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    you can check that this is right by squaring and seeing that you get the same matrix back

  16. satellite73
    • one year ago
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    also you might want to check that i squared the matrix correctly, but i think it is right

  17. satellite73
    • one year ago
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    gotta run

  18. monroe17
    • one year ago
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    okay:) So, the steps to a problem like this is to first follow the formula (A^2=A) for the matrix. Then just solve..

  19. monroe17
    • one year ago
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    when it said A^2=A I first thought it mean like x^2 and 3^2.. i haven't learned this yet lol

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