Write as a Vector Equality y=-3x-3z+11 , x=-2y-z+7 , z=x-y

Problem

y=−3*x−3*z+11,x=−2*y−z+7,z=x−y

Solution

1. Rearrange each equation so that all variables x y and z are on the left side and the constants are on the right side.

3*x+y+3*z=11

x+2*y+z=7

−x+y+z=0

2. Identify the coefficients of the variables to form a system of linear equations in the form A*v=b

([3,1,3],[1,2,1],[−1,1,1])*([x],[y],[z])=([11],[7],[0])

3. Express the system as a linear combination of vectors by using the variables as scalars for the column vectors.

x*([3],[1],[−1])+y*([1],[2],[1])+z*([3],[1],[1])=([11],[7],[0])

Final Answer

x*([3],[1],[−1])+y*([1],[2],[1])+z*([3],[1],[1])=([11],[7],[0])

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