Write as a Vector Equality x+2z=0 , x-y+5z=0 , 2x+y+z=0

Problem

{[x+2*z=0],[x−y+5*z=0],[2*x+y+z=0])

Solution

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

2. Rewrite each equation as a linear combination of the variables by including terms with zero coefficients where necessary.

3. Extract the coefficients of each variable to form column vectors.

4. Express the system as a single vector equation where the variables x y and z scale their respective coefficient vectors.

Final Answer

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

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