Write as a Vector Equality x-y+4z=6 , 2x+z=1 , x+5y+z=-9

Problem

{[x−y+4*z=6],[2*x+z=1],[x+5*y+z=−9])

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, where each vector corresponds to the coefficients of one variable.

3. Assign the variables x y and z as scalars multiplying their respective coefficient vectors.

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

Final Answer

x*[[1],[2],[1]]+y*[[−1],[0],[5]]+z*[[4],[1],[1]]=[[6],[1],[−9]]

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