Write as a Vector Equality 9x-y+z=-31 , 4x+2y-3z=-29 , x-3y+2z=8

Problem

{[9*x−y+z=−31],[4*x+2*y−3*z=−29],[x−3*y+2*z=8])

Solution

1. Identify the coefficients of the variables x y and z for 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 for its corresponding coefficient vector.

3. Set the sum of these scaled vectors equal to the constant vector formed by the values on the right side of the equations.

Final Answer

x*[[9],[4],[1]]+y*[[−1],[2],[−3]]+z*[[1],[−3],[2]]=[[−31],[−29],[8]]

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