Write as a Vector Equality (3x-y+z)=0 , (x-2y+5z)=0 , (-x+y-2z)=0

Problem

{[3*x−y+z=0],[x−2*y+5*z=0],[−x+y−2*z=0])

Solution

1. Identify the variables x y and z as the components of a vector v

2. Extract the coefficients from each equation to form the rows of a coefficient matrix A

3. Represent the system as a single vector equation where the matrix A multiplies the vector of variables to equal the zero vector.

Final Answer

([3,−1,1],[1,−2,5],[−1,1,−2])*([x],[y],[z])=([0],[0],[0])

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