Interpret the rowreduced matrix as the solution of a system

Interpret the row-reduced matrix as the solution of a system of equations: [1 0 0 5 0 1 0 9 0 0 1 2]

Solution

From the row-reduced matrix the solution of a system of equations is ,

1.x + 0.y + 0.z = 5.......................1

0.x + 1.y + 0.z = 9 .........................2

0.x + 0.y + 1.z = 2 ........................3

From equation 1

x = 5

From equation 2

y = 9

From equation 3

z = 2

Therefore ,

The solution is ,

x = 5 , y = 9 , z = 2