Inverse Matrix

Date: 05/05/2003 at 07:49:30
From: Sinan
Subject: Matrices

    x+y+z = 3
      y+z = 2
        z = 1

 The inverse of A: 1 1 1  is A-1: 1 -1 0
                   0 1 1          0  1 -1
                   0 0 1          0  0 1

Use the inverse matrix to find values x, y, and z.

Date: 05/05/2003 at 10:44:55
From: Doctor Luis
Subject: Re: Matrices

Hi Sinan,

You can write your system of equations in the following form:

[ 1 1 1 ]   [ x ]   [ 3 ]
[ 0 1 1 ] * [ y ] = [ 2 ]
[ 0 0 1 ]   [ z ]   [ 1 ]

In matrix notation, (X is a column vector, B is a column vector)

   A * X = B

So, to solve for X, you just "divide" by A by using the inverse A^(-1)

   (A^(-1) * A) * X = (A^(-1)) * B

Since A^(-1) * A is the identity I, and I*X = X, we have

   X = A^(-1) * B

Since you are given the inverse A^(-1), and you already know B, you 
can immediately find the value of X by carrying out the matrix
multiplication.

I hope this helps. Let us know if you have more questions.

- Doctor Luis, The Math Forum
  http://mathforum.org/dr.math/