Write as a Vector Equality 4a+4b+8d=0 , -12a-12b-24d=0 , -6b+18d=0

Problem

{[4*a+4*b+8*d=0],[−12*a−12*b−24*d=0],[−6*b+18*d=0])

Solution

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

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

3. Represent the system as a linear combination of these vectors multiplied by their respective variables.

4. Set the sum of these weighted vectors equal to the zero vector.

Final Answer

a*[[4],[−12],[0]]+b*[[4],[−12],[−6]]+d*[[8],[−24],[18]]=[[0],[0],[0]]

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