Write as a Vector Equality

Problem

{[2*a+b−d−2*g+2*h+j+5*k=21],[a+b−3*d+g+h+j+2*k=−5],[a+2*b−8*d+5*g+h+j−6*k=−15],[3*a+3*b−9*d+3*g+6*h+5*j+2*k=−24],[−2*a−b+d+2*g+h+j−9*k=−30])

Solution

1. Identify the variables in the system of linear equations, which are a,b,d,g,h,j,k

2. Extract the coefficients for each variable to form column vectors.

3. Express the system as a linear combination of these column vectors, where each vector is multiplied by its corresponding variable.

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],[1],[1],[3],[−2]]+b*[[1],[1],[2],[3],[−1]]+d*[[−1],[−3],[−8],[−9],[1]]+g*[[−2],[1],[5],[3],[2]]+h*[[2],[1],[1],[6],[1]]+j*[[1],[1],[1],[5],[1]]+k*[[5],[2],[−6],[2],[−9]]=[[21],[−5],[−15],[−24],[−30]]

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