PROBLEM 12E

Solve the systems in Exercises 11–14.

x1 – 5x2 + 4x3 = –3 |

2x1 – 7x2 + 3x3 = –2 |

– 2x1 + x2 + 7x3 = –1 |

Solution 12E :

Step 1 :we given the system of equations

x1 -5x2 +4x3 = -3

2x1 -7x2+ 3x3 = -2

-2x1 +x2 +7x3 = -1

The system of equation can be return in the form AX = B

Where A is the coefficient matrix , X is the column matrix of unknowns and B is the column matrix of constants.

Step 2 : we have to find the solution of the system

The solution of a system of linear equations can be of three types. They are:-

(i) One solution (ii) Infinite solution and (iii) No solution

Let the augmented matrix of A and B is [A :B], the solution is depend on the rank of augmented matrix and rank of A i.e. and number of unknowns (n)

So we get (i) One solution - if = = (n)

(ii) Infinite solution - if = < (n)

(iii) No solution - if