Write as a Vector Equality

Problem

{[5+(−1)+2*(−8)=−12],[−2*(5)+3*(−1)+3*(−8)=−27],[2*(5)+5*(−1)+(−8)=−3])

Solution

1. Identify the coefficients and the variables (or constants) being multiplied in each equation to form a linear combination.

2. Group the corresponding terms from each equation into column vectors.

3. Factor out the common scalar multipliers from each column vector to represent the system as a sum of scaled vectors.

4. Equate the resulting vector sum to the vector of constants from the right-hand side of the equations.

Final Answer

5*[[1],[−2],[2]]+(−1)*[[1],[3],[5]]+(−8)*[[2],[3],[1]]=[[−12],[−37],[−3]]

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