Write as a Vector Equality

Problem

{[2*x+3*y+z+w=15],[x+y+z+w=2],[2*x+3*y+2*z+w=3],[3*x+y+z+2*w=1])

Solution

1. Identify the coefficients of each variable x y z and w in the system of linear equations.

2. Create column vectors for each variable by grouping their respective coefficients from each equation.

3. Express the system as a linear combination where each variable scales its corresponding coefficient vector.

4. Equate the sum of these scaled vectors to the constant vector formed by the values on the right side of the equations.

Final Answer

x*[[2],[1],[2],[3]]+y*[[3],[1],[3],[1]]+z*[[1],[1],[2],[1]]+w*[[1],[1],[1],[2]]=[[15],[2],[3],[1]]

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