Results 1 to 3 of 3

Math Help - Inverse and Power Matrices

  1. #1
    Junior Member
    Joined
    Oct 2008
    From
    Dallas, TX
    Posts
    71

    Inverse and Power Matrices

    I have a simple 2 x 2 matrix, a =

    -1 2
    1 3

    Correct me if I'm wrong, but the inverse of this matrix is:

    1/5 -2/5
    -1/5 -3/5

    How would I take a^3? Would it be:

    -1^3 2^3
    1^3 3^3

    What would (A^-1)^3 be?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Aug 2008
    Posts
    530
    First calculate A^2= A.A then find A^3 after.

    A^3 will be =A^2.A
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,441
    Thanks
    1862
    Quote Originally Posted by aaronrj View Post
    I have a simple 2 x 2 matrix, a =

    -1 2
    1 3

    Correct me if I'm wrong, but the inverse of this matrix is:

    1/5 -2/5
    -1/5 -3/5
    Yes, you are wrong. It should be fairly easy to see that, multiplying the first row of the first matrix by the first column of the second, (-1)(1/5)+ 2(-1/5)= -3/5 when it should be 1. It looks like you have just divided the numbers in the matrix by the determinant. That does NOT give the inverse matrix.

    How would I take a^3? Would it be:

    -1^3 2^3
    1^3 3^3

    What would (A^-1)^3 be?
    It looks like either you do not know how to multiply matrices or you simply have not thought about multiplying matrices in connection with either of these problems. What is A multiplied by itself?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Raising Matrices to power of n
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: November 12th 2011, 06:59 AM
  2. inverse matrices
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: March 1st 2009, 11:51 AM
  3. inverse matrices
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: December 19th 2008, 11:43 AM
  4. matrices to the power of 100
    Posted in the Algebra Forum
    Replies: 5
    Last Post: April 7th 2008, 07:17 PM
  5. Matrices to a power
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: December 19th 2007, 10:52 AM

Search Tags


/mathhelpforum @mathhelpforum