Write as a Vector Equality x-7+7z=-27 , -6x+y+8z=-38 , 2x+3y+7z=-26

Problem

{[x−7*y+7*z=−27],[−6*x+y+8*z=−38],[2*x+3*y+7*z=−26])

Solution

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

2. Extract the coefficients of x to create the first vector: [[1],[−6],[2]]

3. Extract the coefficients of y to create the second vector: [[−7],[1],[3]]

4. Extract the coefficients of z to create the third vector: [[7],[8],[7]]

5. Identify the constants on the right side of the equations to form the result vector: [[−27],[−38],[−26]]

6. Combine these into a single vector equation where each variable scales its corresponding coefficient vector.

Final Answer

x*[[1],[−6],[2]]+y*[[−7],[1],[3]]+z*[[7],[8],[7]]=[[−27],[−38],[−26]]

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