Examine the consistency of the system of equations`5x y + 4z = 5``2x + 3y + 5z = 2``5x 2y + 6z = 1`

Explanation

Given system of equations,
5x-y+4y=5
2x+3y+5z=2
5x-2y+6z=-1
`rArr" "=[{:(5,-1,4),(2,3,5),(5,-2,6):}][{:(x),(y),(z):}]=[{:(5),(2),(-1):}]rArrAX=B`
`therefore" "A=[{:(5,-1,4),(2,3,5),(5,-2,6):}]`
`rArr" "|A|=[{:(5,-1,4),(2,3,5),(5,-2,6):}]`
=5(18+10)-(-1)(12-25)+4(-4-15)
`=140-13-76=51ne0`
`therefore` A is invertible.
Therefore, given system of eqations is consistent.