Write as a Vector Equality m^2-3mn+n^2=-1 , 3m^2-mn-3n^2=13

Problem

{[m2−3*m*n+n2=−1],[3*m2−m*n−3*n2=13])

Solution

1. Identify the variables and coefficients in the system of equations to represent them as a linear combination of vectors.

2. Rewrite the system by grouping the terms associated with each unique variable combination, which are m2 m*n and n2

3. Express the system as a single vector equation where the coefficients of m2 m*n and n2 form the components of the vectors.

4. Equate the resulting vector sum to the vector containing the constants from the right-hand side of the equations.

Final Answer

m2*([1],[3])+m*n*([−3],[−1])+n2*([1],[−3])=([−1],[13])

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