Write as a Vector Equality

Problem

{[a+0+2*d−g=1],[0+2*b+6*d+2*g=−2],[2*a+0+4*d−2*g=2],[a+b+5*d+0=0])

Solution

1. Identify the variables used in the system of linear equations, which are a b d and g

2. Extract the coefficients for each variable from every equation to form the corresponding column vectors.

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

4. Set the linear combination equal to the vector of constants from the right-hand side of the equations.

Final Answer

a*[[1],[0],[2],[1]]+b*[[0],[2],[0],[1]]+d*[[2],[6],[4],[5]]+g*[[−1],[2],[−2],[0]]=[[1],[−2],[2],[0]]

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