Write as a Vector Equality 2d+3g-h=a , d-g+3h=b , 3d+7g-5h=c

Problem

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

Solution

1. Identify the variables and their coefficients in each equation of the system.

2. Group the coefficients of each variable into separate column vectors.

3. Express the system as a linear combination of these column vectors, where the variables d g and h act as scalars.

4. Equate the resulting vector sum to the vector of constants on the right side of the equations.

Final Answer

d*[[2],[1],[3]]+g*[[3],[−1],[7]]+h*[[−1],[3],[−5]]=[[a],[b],[c]]

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