Write as a Vector Equality x+2y-z=0 , 2x-4y+z=0 , -2x+2y-3z=0

Problem

{[x+2*y−z=0],[2*x−4*y+z=0],[−2*x+2*y−3*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 vectors by multiplying each variable by its corresponding vector of coefficients.

3. Set the sum of these weighted vectors equal to the zero vector on the right side of the equation.

Final Answer

x*[[1],[2],[−2]]+y*[[2],[−4],[2]]+z*[[−1],[1],[−3]]=[[0],[0],[0]]

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