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rsst123

  • one year ago

If A,B,C,D are all invertible nxn matrices,solve for B AB^-1=D? I understand to solve for C you need to multiply each side with the inverse, but I dont understand the premultiply and postmultiply rules

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  1. rsst123
    • one year ago
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    Sorry i typed that wrong its AB^-1C=D solve for B

  2. hartnn
    • one year ago
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    Hello! :) in AB^-1 C = D, you need to isolate B, right?? Also, do you understand that in Matrix algebra, AB and BA are different and not equal everytime?

  3. hartnn
    • one year ago
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    lets take a simpler problem XY = Z isolate Y you would pre multiply by X or post multiply by X?

  4. rsst123
    • one year ago
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    you would multiply each side with X^-1 correct?

  5. rsst123
    • one year ago
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    pre multiply

  6. hartnn
    • one year ago
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    yes, i meant X^-1 sorry, pre multiply or post multiply?

  7. hartnn
    • one year ago
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    ok good

  8. hartnn
    • one year ago
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    if you had post multiplied it, XYX^-1 = Z X^-1 you could not have combined X and X^-1 to get I (the Identity matrix)

  9. hartnn
    • one year ago
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    now lets go to our problem, AB^-1 C = D pre multiply by C or post? :)

  10. hartnn
    • one year ago
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    damn, i mean C^-1 :P

  11. rsst123
    • one year ago
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    haha post right?

  12. hartnn
    • one year ago
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    yes! do it, and post some steps?

  13. rsst123
    • one year ago
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    AB^-1CC^-1=DC^-1 A^-1AB^-1=A^-1DC^-1 I get to B^-1=A^-1DC^-1 but im not sure what i should do from here

  14. hartnn
    • one year ago
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    very good! you solved more than half of it! now take inverse on both sides...

  15. hartnn
    • one year ago
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    and use this recursively, \(\large (PQ)^{-1} = Q^{-1}P^{-1}\)

  16. rsst123
    • one year ago
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    perfect so the answer would be B=D^-1CA ?

  17. hartnn
    • one year ago
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    how did u get that ?

  18. hartnn
    • one year ago
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    \([A^{-1}D C^{-1}]^{-1} = (C^{-1})^{-1} D^{-1} (A^{-1})^{-1} = CD^{-1}A \)

  19. rsst123
    • one year ago
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    oh sorry my bad I was looking at the wrong work I was doing before this is my first time using this site and it's very helpful thank you for your help!!

  20. hartnn
    • one year ago
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    hey, most welcome ^_^ happy to help :) feel free to message me if you wanna ask anything about this site :) \(\Huge \mathcal{\text{Welcome To OpenStudy}\ddot\smile} \)

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