Write as a Vector Equality 2x+4y-2z=-14 , x+2y+4z=3 , x+2y-z=-7

Problem

{[2*x+4*y−2*z=−14],[x+2*y+4*z=3],[x+2*y−z=−7])

Solution

1. Identify the coefficients of the variables x y and z for each equation to form the column vectors.

2. Extract the variables into a single vector of unknowns.

3. Represent the system as a linear combination of vectors by multiplying each variable by its corresponding column of coefficients.

4. Equate the sum of these vectors to the vector of constants from the right-hand side of the equations.

Final Answer

x*[[2],[1],[1]]+y*[[4],[2],[2]]+z*[[−2],[4],[−1]]=[[−14],[3],[−7]]

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