Write as a Vector Equality

Problem

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

Solution

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

2. Rewrite each equation so that all variables are aligned in the same order: w x y and z

3. Extract the coefficients of each variable to form the column vectors for the vector equation.

4. Express the system as a linear combination of these column vectors set equal to the zero vector.

Final Answer

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

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