Write as a Vector Equality 2x+y-4z=0 , x-y+2z=5 , 3x+2y+2z=3

Problem

{[2*x+y−4*z=0],[x−y+2*z=5],[3*x+2*y+2*z=3])

Solution

1. Identify the coefficients of the variables x y and z in each equation of the system.

2. Express the system as a linear combination of constant vectors multiplied by the variables.

3. Group the coefficients of x into the first vector, the coefficients of y into the second vector, and the coefficients of z into the third vector.

4. Set the sum of these vectors equal to the vector containing the constants from the right side of the equations.

Final Answer

x*[[2],[1],[3]]+y*[[1],[−1],[2]]+z*[[−4],[2],[2]]=[[0],[5],[3]]

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