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

Problem

{[−y−z=0],[2*y+2*z=0],[−x+y+2*z=0])

Solution

1. Identify the variables in the system of equations, which are x y and z

2. Rewrite each equation to include all variables by using zero coefficients for missing terms.

0*x−1*y−1*z=0

0*x+2*y+2*z=0

−1*x+1*y+2*z=0

3. Separate the variables into a linear combination of constant vectors multiplied by the scalars x y and z

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

4. Express the system as a matrix-vector product A*v=b where A is the coefficient matrix and v is the vector of variables.

[[0,−1,−1],[0,2,2],[−1,1,2]]*[[x],[y],[z]]=[[0],[0],[0]]

Final Answer

[[0,−1,−1],[0,2,2],[−1,1,2]]*[[x],[y],[z]]=[[0],[0],[0]]

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