Write as a Vector Equality

Problem

{[7*x+2*y+2*z=−46],[−7*x+4*y+2*z=0],[8*x+4*y+4*z=−68])

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 result vector.

3. Express the system as a linear combination of vectors by multiplying each variable by its corresponding column of coefficients.

4. Combine the terms into a single vector equality where the sum of the scaled vectors equals the constant vector.

Final Answer

x*[[7],[−7],[8]]+y*[[2],[4],[4]]+z*[[2],[2],[4]]=[[−46],[0],[−68]]

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