Write as a Vector Equality x+2y-z=2 , 2x-2y+z=-1 , 6x+4y+3z=5

Problem

{[x+2*y−z=2],[2*x−2*y+z=−1],[6*x+4*y+3*z=5])

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 by multiplying each vector by its corresponding variable.

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],[6]]+y*[[2],[−2],[4]]+z*[[−1],[1],[3]]=[[2],[−1],[5]]

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