PLEASE HELP! Linear Equation geometric description?

Posted on 2015-12-09 06:42:00 in Chemistry by GEORGE

Consider the system of equations
x + 2y - z = - 3
3x + 5y + kz = - 4
9x + (k + 13)y + 6z = 9

(a) Express these equations as an augmented matrix. 

(b) Show that this matrix can be row-reduced to:

[ 1 2 -1 | - 3
0 1 -k -3 | - 5
0 0 k^2 - 2k | 5k + 11 ]

(c) Hence answer the following questions.

(i) For what value(s) of k does the system have 

- no solutions ? 

- a unique solution ? 

- infinitely many solutions ?

(ii) ?Each of these equations represents a plane. In each case in (i), give a geometric description of the intersection of the three planes.

I just need help on question C part 2 (ii), my teacher also added that I had to find out if there are any parallel planes by using row operations to change the orientation of the planes but keep the solution set the same, this confuses me. 

If anyone could please help me to understand this part and show there working out. That would be amazing and I appreciate it very much

 

 

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