Write as a Vector Equality x+y+z=2 , 4x+5y+z=12 , 2x=-4

Problem

{[x+y+z=2],[4*x+5*y+z=12],[2*x=−4])

Solution

1. Identify the coefficients of the variables x y and z in each equation of the system.

2. Express the system as a linear combination of constant vectors multiplied by the variables x y and z

3. Construct the vector equality by setting the sum of these scaled vectors equal to the vector of constants from the right-hand side of the equations.

Final Answer

x*[[1],[4],[2]]+y*[[1],[5],[0]]+z*[[1],[1],[0]]=[[2],[12],[−4]]

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