Write as a Vector Equality 2x-y+z=5 , 3x+2y-z=-1 , x-y-z=0

Problem

{[2*x−y+z=5],[3*x+2*y−z=−1],[x−y−z=0])

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 linear combination equal to the vector of constants from the right-hand side of the equations.

Final Answer

x*[[2],[3],[1]]+y*[[−1],[2],[−1]]+z*[[1],[−1],[−1]]=[[5],[−1],[0]]

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