#### Question

# What is the complete solution of linear system for x-2y-3z=6, 2x+y-z=6, 4x-3y-7z=6?

I am stuck I got for answers were x=47/5, y= 1/5 z=1 but its wrong. Can anyone clarify how to solve this problem. Thankyou for your time.

#### Answers

We would first start by setting all of our data into a matrix equation, then label each matrice.

A X B

|1 -2 -3||x| |6|

|2 1 -1||y|=|6|

|4 -3 -7||z| |6|

Which gives us the equation AX=B. To solve for X we must multiply A and B by the inverse of A to give us an equation like X=A'B. Since the inverse of A starts by multiplying 1/|A| we should solve for the determinant of A. If it is 0 then there are no solutions.

|A|=(-7)+(8)+(18)-(-12)-(28)-(3)

|A|=0

Therefore there are no solutions for this linear system.

We could also do this algebraically which would give us no solutions.

is this stupid thing from this world?

hey i think i can solve this but is too hard to explain it here .. i am so so so sorry