Write as a Vector Equality a+b-d=2 , 3a+3b+d=2 , a+d=0

Problem

{[a+b−d=2],[3*a+3*b+d=2],[a+d=0])

Solution

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

2. Rewrite each equation so that all variables are represented, using zero coefficients where necessary.

1*a+1*b−1*d=2

3*a+3*b+1*d=2

1*a+0*b+1*d=0

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

4. Express the system as a linear combination of these column vectors multiplied by their respective variables.

a*[[1],[3],[1]]+b*[[1],[3],[0]]+d*[[−1],[1],[1]]=[[2],[2],[0]]

Final Answer

a*[[1],[3],[1]]+b*[[1],[3],[0]]+d*[[−1],[1],[1]]=[[2],[2],[0]]

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