(1.2: Solving linear equations) Consider the linear system2x1+ 3x2−5x3=b17x1+ 2x2+ 8x3=b2−x1+x2−5x3=b3(a) Find the echelon form of the augmented matrix of the above system.(b) Find the conditions onb1,b2,b3for which this system has a solution.(c) Do you see the shape of the points (b1,b2,b3) for which the above system has asolution?(d) If you randomly pick

Echelon form of augmented matrix      

Step-by-step explanation:

We have, linear systems

 Find the echelon form of the augmented matrix.

Firstly we find the augmented matrix (A) of the given linear system

Now find the echelon form

 From above echelon form of augmented matrix system is consistent .

So, system has always a solution exist for every condition of

 Yes, If we take point   then system of linear equation has exist a solution.

  yes, if pick randomly then always exist a solution of given system of linear equation.

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answer:

c) the x-coordinate of the center of the circle increases by 3