Write as a Vector Equality x+y+z+w=15 , x-2y+4z-w=12

Problem

{[x+y+z+w=15],[x−2*y+4*z−w=12])

Solution

1. Identify the variables involved in the system of linear equations, which are x y z and w

2. Extract the coefficients for each variable from both equations to form column vectors.

3. Express the system as a linear combination of these column vectors, where each variable scales its corresponding coefficient vector.

4. Set the resulting vector sum equal to the vector containing the constants from the right-hand side of the equations.

Final Answer

x*[[1],[1]]+y*[[1],[−2]]+z*[[1],[4]]+w*[[1],[−1]]=[[15],[12]]

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