Write as a Vector Equality -x+y+2x=-10 , x+y-z=7 , 2x+y+z=5

Problem

{[−x+y+2*z=−10],[x+y−z=7],[2*x+y+z=5])

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 for its corresponding coefficient vector.

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

Final Answer

x*[[−1],[1],[2]]+y*[[1],[1],[1]]+z*[[2],[−1],[1]]=[[−10],[7],[5]]

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