Question

Determine conditions on a, b and c so that the following system has solutions:

2x + y + z = a

x − 2y + z = b

3x − y + 2z = c

Can you please show all the steps to help me understand how the problem was solved.

Answer 1

Given system of equation ,

The coefficient matrix is hoben by ,

Now det(A) = 2(-4+1)-1(2-3)+1(-1+6)=0

So the matrix has rank , as first two row are independent. So exactly one row can be written as linear combination of two other .

Now , 3x-y+2z=(2x+y+z)+(x-2y+z)

Hence the required condition on a , b , c for which solution exist is ,