Write as a Vector Equality x+2y-z=4 , 3x-y+7z=-3 , 4x+y+6z=1

Problem

{[x+2*y−z=4],[3*x−y+7*z=−3],[4*x+y+6*z=1])

Solution

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

2. Extract the x coefficients from the left side of the system to create the first vector: ([1],[3],[4])

3. Extract the y coefficients from the left side of the system to create the second vector: ([2],[−1],[1])

4. Extract the z coefficients from the left side of the system to create the third vector: ([−1],[7],[6])

5. Identify the constants on the right side of the equations to form the result vector: ([4],[−3],[1])

6. Combine these into a linear combination where each variable scales its corresponding coefficient vector.

Final Answer

x*([1],[3],[4])+y*([2],[−1],[1])+z*([−1],[7],[6])=([4],[−3],[1])

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