Write as a Vector Equality

Problem

{[w−x+y+z=−5],[4*w−3*x−4*y+2*z=−37],[3*w+x−3*y−3*z=−11],[−w+2*x+2*y+2*z=6])

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 column vectors.

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

4. Equate this linear combination to the column vector formed by the constants on the right side of the equations.

Final Answer

w*[[1],[4],[3],[−1]]+x*[[−1],[−3],[1],[2]]+y*[[1],[−4],[−3],[2]]+z*[[1],[2],[−3],[2]]=[[−5],[−37],[−11],[6]]

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