Write as a Vector Equality x+y+z=6 , 2x+y-3z=-5 , 3x-2y+z=2

Problem

{[x+y+z=6],[2*x+y−3*z=−5],[3*x−2*y+z=2])

Solution

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

2. Express the system as a linear combination of these column vectors, where each variable acts as a scalar multiplier.

3. Set the sum of these scaled vectors equal to the vector of constants from the right-hand side of the equations.

Final Answer

x*[[1],[2],[3]]+y*[[1],[1],[−2]]+z*[[1],[−3],[1]]=[[6],[−5],[2]]

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