Write as a Vector Equality x+2y+x=4 , x-y=1 , x+3y=0

Problem

{[x+2*y+x=4],[x−y=1],[x+3*y=0])

Solution

1. Simplify the first equation by combining the like terms x and x to get 2*x+2*y=4

2. Identify the coefficients of the variables x and y for each equation to form the column vectors.

3. Extract the variable x from the first column of coefficients to create the first vector component x*[[2],[1],[1]]

4. Extract the variable y from the second column of coefficients to create the second vector component y*[[2],[−1],[3]]

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

Final Answer

x*[[2],[1],[1]]+y*[[2],[−1],[3]]=[[4],[1],[0]]

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