Write as a Vector Equality x+2y-4z=4 , -3x-6y+12z=-12

Problem

{[x+2*y−4*z=4],[−3*x−6*y+12*z=−12])

Solution

1. Identify the variables and coefficients in the system of linear equations. The variables are x y and z

2. Extract the coefficient vectors for each variable from the left side of the equations.

3. Form the vector equation by multiplying each variable by its corresponding coefficient vector and setting the sum equal to the constant vector from the right side.

4. Observe that the second equation is a multiple of the first (multiplied by −3, which means the vectors are linearly dependent, but the task is to represent the system as a single vector equality.

Final Answer

x*[[1],[−3]]+y*[[2],[−6]]+z*[[−4],[12]]=[[4],[−12]]

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