1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Matrix Algebra Equation

  1. May 18, 2015 #1
    1. The problem statement, all variables and given/known data
    Given the matrices A, B, C, D, X are invertible such that
    Find an expression for X.

    2. Relevant equations
    Answer is [tex]A^{-1}CAC^{-1}-A^{-1}BD[/tex]

    3. The attempt at a solution
    I know you can't do normal algebra for matrices.
    So this means A≠(AX+BD)?
  2. jcsd
  3. May 18, 2015 #2


    User Avatar
    Science Advisor

    Your last question puzzles me [itex]A\ne AX+ BD[/itex], unless X= 1 and B or D= 0, for numbers, much less matrices! (Oh, I see- no, you cannot just "cancel" C.)

    You can do "normal algebra" for matrices as long as you remember that matrix multiplication is not commutative, that some matrices do not have multiplicative inverses, and we say "multiply by A-1" not "divide by A". Here, we are told that every matrix is invertible.

    From (AX+ BD)C= CA, we "unpeel" X just as we would for numbers. The quantity on the left of the equation is multiplied by, on the right, by C. So start by multiplying both sides of the equation, on the right, by C-1. Continue from there.
  4. May 18, 2015 #3


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    Instead of worrying about whether A = (AX + BD), why don't you use the rules of matrix algebra (which you know, I assume) to find X?

    Start off by expanding the original matrix equation.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted