Write as a Vector Equality x+4y+2z=6 , x+y+z=0 , -x-4y+3z=-6

Problem

{[x+4*y+2*z=6],[x+y+z=0],[−x−4*y+3*z=−6])

Solution

1. Identify the coefficients of the variables x y and z in each equation to form the column vectors.

2. Extract the variable x from the first terms to create the first vector:

x*[[1],[1],[−1]]

3. Extract the variable y from the second terms to create the second vector:

y*[[4],[1],[−4]]

4. Extract the variable z from the third terms to create the third vector:

z*[[2],[1],[3]]

5. Set the sum of these vectors equal to the vector of constants from the right side of the equations.

Final Answer

x*[[1],[1],[−1]]+y*[[4],[1],[−4]]+z*[[2],[1],[3]]=[[6],[0],[−6]]

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