Write as a Vector Equality x+2y-z=-9 , x+z=5 , 2x-y-z=-11

Problem

{[x+2*y−z=−9],[x+z=5],[2*x−y−z=−11])

Solution

1. Identify the coefficients of the variables x y and z for each equation in the system.

2. Represent the system as a linear combination of constant vectors scaled by the variables x y and z

3. Extract the column vectors from the coefficients: the first vector contains coefficients of x the second contains coefficients of y and the third contains coefficients of z

4. Equate the sum of these scaled vectors to the vector of constants from the right-hand side of the equations.

Final Answer

x*[[1],[1],[2]]+y*[[2],[0],[−1]]+z*[[−1],[1],[−1]]=[[−9],[5],[−11]]

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