Write as a Vector Equality x+y+z=-9 , x-y+5z=-19 , 5x+y+z=-29

Problem

{[x+y+z=−9],[x−y+5*z=−19],[5*x+y+z=−29])

Solution

1. Identify the coefficients of the variables x y and z for 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],[1],[5])

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

4. Extract the variable z from the third terms of each equation to create the third vector: z*([1],[5],[1])

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

Final Answer

x*([1],[1],[5])+y*([1],[−1],[1])+z*([1],[5],[1])=([−9],[−19],[−29])

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