Write as a Vector Equality x-y=6 , 2y-z=-1 , 5x+5+z=7

Problem

{[x−y=6],[2*y−z=−1],[5*x+5+z=7])

Solution

1. Rearrange the third equation to isolate the variables on one side and the constant on the other.

5*x+z=7−5

5*x+z=2

2. Align the variables x y and z in each equation, using zero coefficients for missing terms.

1*x−1*y+0*z=6

0*x+2*y−1*z=−1

5*x+0*y+1*z=2

3. Extract the coefficients of each variable to form the column vectors for the vector equation.

x*([1],[0],[5])+y*([−1],[2],[0])+z*([0],[−1],[1])=([6],[−1],[2])

Final Answer

x*([1],[0],[5])+y*([−1],[2],[0])+z*([0],[−1],[1])=([6],[−1],[2])

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