Inverse MatrixDate: 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/ |
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