Write as a Vector Equality a+b+d=7 , a-b+2d=7 , 5a+b+d=11

Problem

{[a+b+d=7],[a−b+2*d=7],[5*a+b+d=11])

Solution

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

2. Extract the coefficients of each variable from each equation to form the component vectors.

3. Express the system as a linear combination of these component vectors, where each variable scales its corresponding vector of coefficients.

4. Equate the sum of these scaled vectors to the vector formed by the constants on the right-hand side of the equations.

Final Answer

a*[[1],[1],[5]]+b*[[1],[−1],[1]]+d*[[1],[2],[1]]=[[7],[7],[11]]

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