Write as a Vector Equality x+y+z=6 , 2y+5z=-4 , 2x+5y-z=27

Problem

{[x+y+z=6],[2*y+5*z=−4],[2*x+5*y−z=27])

Solution

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

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

3. Extract the column vectors from the coefficients: for x the coefficients are 1 0 and 2 for y they are 1 2 and 5 for z they are 1 5 and −1

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],[0],[2]]+y*[[1],[2],[5]]+z*[[1],[5],[−1]]=[[6],[−4],[27]]

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