Write as a Vector Equality x+y-z=-6 , -x+z=4 , y+2z=8

Problem

{[x+y−z=−6],[−x+z=4],[y+2*z=8])

Solution

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

2. Rewrite each equation so that all variables are represented, using a coefficient of 0 for any missing variables.

1*x+1*y−1*z=−6

−1*x+0*y+1*z=4

0*x+1*y+2*z=8

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

4. Express the system as a linear combination of these column vectors multiplied by their respective variables, set equal to the constant vector.

Final Answer

x*[[1],[−1],[0]]+y*[[1],[0],[1]]+z*[[−1],[1],[2]]=[[−6],[4],[8]]

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