Write as a Vector Equality x+y-z=-7 , 6x-y+z=-28 , -x+3y-2z=-1

Problem

{[x+y−z=−7],[6*x−y+z=−28],[−x+3*y−2*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 coefficients of x from each equation to create the first vector: ([1],[6],[−1])

3. Extract the coefficients of y from each equation to create the second vector: ([1],[−1],[3])

4. Extract the coefficients of z from each equation to create the third vector: ([−1],[1],[−2])

5. Identify the constants on the right side of the equations to form the result vector: ([−7],[−28],[−1])

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

Final Answer

x*([1],[6],[−1])+y*([1],[−1],[3])+z*([−1],[1],[−2])=([−7],[−28],[−1])

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