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

Problem

{[x+y+2*z=1],[x+z=2],[−y−z=1])

Solution

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

2. Extract the coefficients of each variable from each equation to form the column vectors.

3. Write the system as a linear combination of these column vectors multiplied by their respective variables.

4. Set the sum of these vectors equal to the constant vector formed by the values on the right side of the equations.

Final Answer

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

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