Write as a Vector Equality x+y+z=4 , 2x-3y+z=1 , 2x+y-z=1

Problem

{[x+y+z=4],[2*x−3*y+z=1],[2*x+y−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 coefficients of x from each equation to create the first vector: ([1],[2],[2])

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

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

5. Set the linear combination of these vectors equal to the vector of constants from the right-hand side of the equations.

Final Answer

x*([1],[2],[2])+y*([1],[−3],[1])+z*([1],[1],[−1])=([4],[1],[1])

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