Write as a Vector Equality

Problem

{[2*w+3*x−y−z=9],[w+x−y−z=0],[6*w+x−2*y−z=4],[−w+2*x+3*y−z=5])

Solution

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

2. Extract the coefficients of each variable from the left side of the equations to form the column vectors.

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

4. Equate the resulting vector sum to the vector of constants from the right side of the equations.

Final Answer

w*[[2],[1],[6],[−1]]+x*[[3],[1],[1],[2]]+y*[[−1],[−1],[−2],[3]]+z*[[−1],[−1],[−1],[−1]]=[[9],[0],[4],[5]]

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