Write as a Vector Equality a-d=5 , 2a+2b+2d=8 , b+4d=-6

Problem

{[a−d=5],[2*a+2*b+2*d=8],[b+4*d=−6])

Solution

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

2. Rewrite each equation so that all variables are present, using a coefficient of 0 for any missing variables.

1*a+0*b−1*d=5

2*a+2*b+2*d=8

0*a+1*b+4*d=−6

3. Separate the system into a linear combination of constant vectors, where each vector is multiplied by one of the variables.

a*[[1],[2],[0]]+b*[[0],[2],[1]]+d*[[−1],[2],[4]]=[[5],[8],[−6]]

Final Answer

a*[[1],[2],[0]]+b*[[0],[2],[1]]+d*[[−1],[2],[4]]=[[5],[8],[−6]]

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