Write as a Vector Equality 6x-y+3z=-11 , x+3y-z=3 , 3x+3y-4z=-4

Problem

{[6*x−y+3*z=−11],[x+3*y−z=3],[3*x+3*y−4*z=−4])

Solution

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

2. Extract the constants from the right-hand side of the equations to form the constant vector.

3. Express the system as a linear combination of the variable vectors, where each variable scales a vector of its corresponding coefficients.

4. Combine the terms into a single vector equality by setting the sum of the scaled vectors equal to the constant vector.

Final Answer

x*[[6],[1],[3]]+y*[[−1],[3],[3]]+z*[[3],[−1],[−4]]=[[−11],[3],[−4]]

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