Write as a Vector Equality a+2b=1 , 2a+d=2 , 3a+2b+d-g=4

Problem

{[a+2*b=1],[2*a+d=2],[3*a+2*b+d−g=4])

Solution

1. Identify the variables present in the system of equations, which are a b d and g

2. Rewrite each equation so that all variables are represented, using a coefficient of 0 for any missing variables.

1*a+2*b+0*d+0*g=1

2*a+0*b+1*d+0*g=2

3*a+2*b+1*d−1*g=4

3. Decompose the system into a linear combination of vectors by factoring out each variable as a scalar multiplier for a column vector of its coefficients.

a*([1],[2],[3])+b*([2],[0],[2])+d*([0],[1],[1])+g*([0],[0],[−1])=([1],[2],[4])

Final Answer

a*([1],[2],[3])+b*([2],[0],[2])+d*([0],[1],[1])+g*([0],[0],[−1])=([1],[2],[4])

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