Write as a Vector Equality x+3y-6z=7 , 2x-y+2z=0

Problem

{[x+3*y−6*z=7],[2*x−y+2*z=0])

Solution

1. Identify the variables x y and z as the scalars that multiply the column vectors of the coefficients.

2. Extract the coefficients from each equation to form the vectors for each variable.

3. Represent the system as a linear combination of these vectors set equal to the vector of constants.

4. Construct the final vector equation by placing the coefficients of x in the first vector, y in the second, and z in the third.

Final Answer

x*[[1],[2]]+y*[[3],[−1]]+z*[[−6],[2]]=[[7],[0]]

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