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

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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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