Simultaneous Equations with More than Two Unknowns

In Chapter 3, we discussed the use of the method of substitution and the method of elimination to solve the linear inhomogeneous set of two simultaneous equations  

This method is a systematic method for solving linear inhomogeneous equations. We illustrate the method with the set of two linear inhomogeneous equations in Eq. (10.1). Written in matrix form these equations are 

EXERCISE 10.1 Use the rules of matrix multiplication to show that Eq. (10.2) is identical with Eq. (10.1). Q 

Cramer s rule states that the solutions to this set of equations are written as quotients of determinants  

The solutions are constructed as follows The denominator in each expression is the determinant of the matrix A, and the numerator is the determinant of this matrix with one of the columns replaced by the column vector. In the expression for X, the column of coefficients for x is replaced, and in the expression for y, the column of coefficients for y is replaced. 

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Simultaneous Equations with More than Two Unknowns... 

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