Write as a Vector Equality x+y+z=-4 , 2x+4y+2z=-20 , -x+6y-3z=-48

Problem

{[x+y+z=−4],[2*x+4*y+2*z=−20],[−x+6*y−3*z=−48])

Solution

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

2. Extract the coefficients of each variable from the left side of the equations to form the column vectors.

3. Represent the system as a linear combination of these column vectors, where each variable scales its respective coefficient vector.

4. Equate the sum of these scaled vectors to the vector formed by the constants on the right side of the equations.

Final Answer

x*[[1],[2],[−1]]+y*[[1],[4],[6]]+z*[[1],[2],[−3]]=[[−4],[−20],[−48]]

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