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

Problem

{[2*x+3*y−z=6],[x−2*y+z=−1],[3*x+y−3*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 (2,1,3) the y coefficients (3,−2,1) and the z coefficients (−1,1,−3)

3. Write each set of coefficients as a vector multiplied by its corresponding variable.

4. Set the sum of these vectors equal to the vector of constants from the right-hand side of the equations (6,−1,−1)

Final Answer

x*[[2],[1],[3]]+y*[[3],[−2],[1]]+z*[[−1],[1],[−3]]=[[6],[−1],[−1]]

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