Write as a Vector Equality x+2z=5 , 2x+3y+z=9 , 3y-z=11

Problem

{[x+2*z=5],[2*x+3*y+z=9],[3*y−z=11])

Solution

1. Identify the variables present in the system of linear equations, which are x y and z

2. Rewrite each equation so that all variables are represented, using a coefficient of 0 for any missing terms.

1*x+0*y+2*z=5

2*x+3*y+1*z=9

0*x+3*y−1*z=11

3. Decompose the system into a linear combination of constant vectors multiplied by their respective variables.

x*[[1],[2],[0]]+y*[[0],[3],[3]]+z*[[2],[1],[−1]]=[[5],[9],[11]]

Final Answer

x*[[1],[2],[0]]+y*[[0],[3],[3]]+z*[[2],[1],[−1]]=[[5],[9],[11]]

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