Write as a Vector Equality x-y+z=-8 , 3x+2y-z=13 , -2x+3y-z=27

Problem

{[x−y+z=−8],[3*x+2*y−z=13],[−2*x+3*y−z=27])

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],[3],[−2])

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

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

5. Identify the constants on the right side of the equations to form the result vector: ([−8],[13],[27])

6. Combine these into a linear combination where the variables x y and z scale their respective coefficient vectors.

Final Answer

x*([1],[3],[−2])+y*([−1],[2],[3])+z*([1],[−1],[−1])=([−8],[13],[27])

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