Question

Find all values of 'k' for which
kx+4y+z=0
4x+ky+2z=0
2x+2y+z=0
have a common line of intersection .
Please explain in detail .

Answer 1

solve q3 for z then put the value in eq 1

Answer 2

and put into 2

Answer 3

you should get
kx+4y -2x-2y=0
4x+ky+2(-2x-2y)=0

Answer 4

eq(1) kx+2y-2x=0
eq(2) ky-4y=0
y(k-4)=0 , y=0 or k=4

Answer 5

(4)x+2y-2x=0
2x+2y=0 ----> x=-y

Answer 6

Ahaa !
Thanks a lot ! :D
This question was asked in the chapter vectors and 3-D , Do you think there is any other approach possible to this question ?

Answer 7

@AJ01

Answer 8

when 3 planes intersects at a line, the rank of the augmented matrix must be 2.

Answer 9

To get it, among 3 equations, you must have one of them is the multiple of the other one. Try it

Answer 10

I believe that you have Linear Algebra course, right? If not, you don't have this question. It is about either linear algebra or calculus3 (dealing with planes)

Answer 11

Umm , I do not really understand much of what you are saying .
I do not have these course , but could you still please try to explain it to me ?

Answer 12

http://www.emathematics.net/posreltresplanos.php