Write as a Vector Equality x+y-z=4 , 2x+z=7 , 3x-2y=5

Problem

{[x+y−z=4],[2*x+z=7],[3*x−2*y=5])

Solution

1. Identify the coefficients of the variables x y and z in each equation of the system.

2. Express each equation as a linear combination of the variables by separating the terms into vectors corresponding to each variable.

3. Factor out the scalar variables x y and z from their respective coefficient vectors.

4. Equate the sum of these scaled vectors to the vector containing the constants from the right-hand side of the equations.

Final Answer

x*[[1],[2],[3]]+y*[[1],[0],[−2]]+z*[[−1],[1],[0]]=[[4],[7],[5]]

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