Write as a Vector Equality 4a-b-3c=27 , -4a-4b-2c=32 , 4a+9b+7c=37

Problem

{[4*a−b−3*c=27],[−4*a−4*b−2*c=32],[4*a+9*b+7*c=37])

Solution

1. Identify the coefficients of each variable a b and c in the system of linear equations.

2. Express the system as a linear combination of column vectors, where each variable scales a vector containing its respective coefficients from each equation.

3. Set the sum of these scaled vectors equal to the vector containing the constants from the right-hand side of the equations.

Final Answer

a*[[4],[−4],[4]]+b*[[−1],[−4],[9]]+c*[[−3],[−2],[7]]=[[27],[32],[37]]

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