Write as a Vector Equality x+2y-z=1 , 2x-y+z=3 , -x+2y+3z=7

Problem

{[x+2*y−z=1],[2*x−y+z=3],[−x+2*y+3*z=7])

Solution

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

2. Extract the variable x from the first terms of each equation to create the first vector: x*([1],[2],[−1])

3. Extract the variable y from the second terms of each equation to create the second vector: y*([2],[−1],[2])

4. Extract the variable z from the third terms of each equation to create the third vector: z*([−1],[1],[3])

5. Set the sum of these vectors equal to the vector of constants from the right side of the equations.

Final Answer

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

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