Write as a Vector Equality 2x+3y-z=0 , x+2y+4z=0 , x-14z=0

Problem

{[2*x+3*y−z=0],[x+2*y+4*z=0],[x−14*z=0])

Solution

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

2. Rewrite each equation as a linear combination of the variables x y and z by explicitly showing coefficients of zero where a variable is missing.

3. Separate the system into a sum of vectors, where each vector corresponds to one variable multiplied by its coefficients from the equations.

4. Express the system as a single vector equation by setting the sum of these variable-scaled vectors equal to the zero vector.

Final Answer

x*[[2],[1],[1]]+y*[[3],[2],[0]]+z*[[−1],[4],[−14]]=[[0],[0],[0]]

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