Write as a Vector Equality 2x+b-3c=12 , 5a-4b+7c=27 , 10a+3b-c=40

Problem

{[2*a+b−3*c=12],[5*a−4*b+7*c=27],[10*a+3*b−c=40])

Solution

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

2. Separate the coefficients of each variable into distinct column vectors.

3. Express the system as a linear combination where each variable scales its corresponding coefficient vector.

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

Final Answer

a*[[2],[5],[10]]+b*[[1],[−4],[3]]+c*[[−3],[7],[−1]]=[[12],[27],[40]]

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