Write as a Vector Equality

Problem

{[a−4*b+2*d+3*g=5],[2*a−7*b+4*d+g=9],[a−3*b+2*d−2*g=4])

Solution

1. Identify the variables and their coefficients from the system of linear equations. The variables are a b d and g

2. Extract the coefficient vectors for each variable by looking at the columns of the system.

a*([1],[2],[1]),b*([−4],[−7],[−3]),d*([2],[4],[2]),g*([3],[1],[−2])

3. Identify the constant vector from the right-hand side of the equations.

([5],[9],[4])

4. Construct the vector equality by summing the products of each variable and its corresponding coefficient vector and setting it equal to the constant vector.

a*([1],[2],[1])+b*([−4],[−7],[−3])+d*([2],[4],[2])+g*([3],[1],[−2])=([5],[9],[4])

Final Answer

a*([1],[2],[1])+b*([−4],[−7],[−3])+d*([2],[4],[2])+g*([3],[1],[−2])=([5],[9],[4])

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