In Exercises 1 through 12, find all solutions of the equations with paper and pencil using Gauss–Jordan elimination. Show all your work.
For the given system of equation are free variables and
First of all we will make the augmented matrix to the corresponding system of equations.
The corresponding augmented matrix is written as:
The above augmented matrix obtained above is already in reduced form, then the
System of equation to the corresponding above matrix will be
According to system , the variables depend on are free variables.
Thus, for the given system of equation are free variables and .
Consider a solutionof the linear system. Justify the facts stated in parts (a) and (b):
a. Ifis a solution of the system, then is a solution of the system .
b. Ifis another solution of the system, thenis a solution of the system .
c. Now suppose A is amatrix. A solution vectorof the systemis shown in the accompanying figure. We are told that the solutions of the systemform the line shown in the sketch. Draw the line consisting of all solutions of the system.
If you are puzzled by the generality of this problem, think about an example first:
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