College Algebra Matrices
Systems of Equations: Use of Matrix Inverses
   Concepts 1

Statement 
.
Using matrix multiplication and equality, we can wtite a system of n linear equations in the n unknowns, x1, x2,..., xn,
as the matrix equation
or
AX=B,
where A=(aij)n x n, X=(xi)n x 1, B=(bi)n x 1. If A-1 exists, we can solve the matrix equation by multiplying both sides of the equation by A-1. It gives
X=A-1B.

Example 1. Find the solution of the system of three linear equations in three unknowns using matrix inverses:

Solution
Matrix
  will be the inverse matrix of the matrix of the coefficients
 .

Since X=A-1B, we have
 .

Answer:   


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