Write as a Vector Equality x-y+z=6 , x+y+z=2 , x+y-z=0

Problem

{[x−y+z=6],[x+y+z=2],[x+y−z=0])

Solution

1. Identify the coefficients of the variables x y and z in each equation to form the coefficient matrix A

2. Define the vector of variables x as a column vector containing x y and z

3. Extract the constants from the right-hand side of the equations to form the constant vector b

4. Construct the vector equality by multiplying the coefficient matrix by the variable vector and setting it equal to the constant vector.

Final Answer

[[1,−1,1],[1,1,1],[1,1,−1]]*[[x],[y],[z]]=[[6],[2],[0]]

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