Show that the three planes x + y + z = 2 , -x - y + 4z = 3 and x + y + 2z = 3

Question

intersect in a line, and find the equation of that line.? 

 

 

Answer 1

The planes are

π₁: x + y + z = 2 

π₂: -x - y + 4z = 3

π₃: x + y + 2z = 3

So Rank of M is 2

So Rank of M' is 2

Rank of M and rank of M' is 2.

 

So they intersect in a line.

Answer 2

ind the augmented matrix:

Reduce the matrix.

z = 1

x + y +2 z =1

x + y =-1