Write as a Vector Equality x+y-z=-5 , 2x-y+z=5 , -x+5y-4z=1

Problem

{[x+y−z=−5],[2*x−y+z=5],[−x+5*y−4*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 variable x from the first terms of each equation to create the first vector: x*([1],[2],[−1])

3. Extract the variable y from the second terms of each equation to create the second vector: y*([1],[−1],[5])

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

5. Set the sum of these scaled vectors equal to the vector of constants from the right side of the equations.

Final Answer

x*([1],[2],[−1])+y*([1],[−1],[5])+z*([−1],[1],[−4])=([−5],[5],[1])

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