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

Problem

{[2*x+3*y=0],[x=0],[−x−2*y=0])

Solution

1. Identify the coefficients of the variables x and y in each equation to form the column vectors.

2. Extract the coefficients of x from the system to create the first vector:

x*[[2],[1],[−1]]

3. Extract the coefficients of y from the system to create the second vector (note that the second equation has 0*y:

y*[[3],[0],[−2]]

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

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

Final Answer

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

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