Write as a Vector Equality

Problem

{[2*x−y+3*z−w=−3],[3*x+2*y−z+w=13],[x−3*y+z−2*w=−4],[−x+y+4*z+3*w=0])

Solution

1. Identify the coefficients of each variable x y z and w in every equation to form the column vectors.

2. Express the system as a linear combination of these column vectors, where each variable acts as a scalar multiplier for its corresponding vector of coefficients.

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

Final Answer

x*[[2],[3],[1],[−1]]+y*[[−1],[2],[−3],[1]]+z*[[3],[−1],[1],[4]]+w*[[−1],[1],[−2],[3]]=[[−3],[13],[−4],[0]]

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