Write as a Vector Equality x-y-z=0 , 2x-y+2z=1 , x-y+z=-2

Problem

{[x−y−z=0],[2*x−y+2*z=1],[x−y+z=−2])

Solution

1. Identify the coefficients of the variables x y and z in each equation to form the column vectors.

2. Extract the coefficients of x from the system to create the first vector:

([1],[2],[1])

3. Extract the coefficients of y from the system to create the second vector:

([−1],[−1],[−1])

4. Extract the coefficients of z from the system to create the third vector:

([−1],[2],[1])

5. Identify the constants on the right side of the equations to form the result vector:

([0],[1],[−2])

6. Combine these into a single vector equation where the variables scale their respective coefficient vectors.

Final Answer

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

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