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

Problem

{[x+y=2],[y−2*z=3],[x−2=0])

Solution

1. Rearrange the equations to align the variables x y and z on the left side and constants on the right side.

x+y+0*z=2

0*x+y−2*z=3

x+0*y+0*z=2

2. Identify the coefficients of each variable to form a coefficient matrix A

A=[[1,1,0],[0,1,−2],[1,0,0]]

3. Define the variable vector x and the constant vector b

x=[[x],[y],[z]]

b=[[2],[3],[2]]

4. Construct the vector equality by expressing the system in the form A*x=b

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

Final Answer

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

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