Write as a Vector Equality x+5z=0 , y+2z=0 , w=0

Problem

{[x+5*z=0],[y+2*z=0],[w=0])

Solution

1. Identify the variables involved in the system of equations, which are x y z and w

2. Express each variable in terms of the free variable z by rearranging the equations.

x=−5*z

y=−2*z

z=z

w=0

3. Construct the solution vector v by placing the expressions for each variable into a column vector.

v=[[x],[y],[z],[w]]=[[−5*z],[−2*z],[z],[0]]

4. Factor out the scalar variable z to write the system as a vector equality.

[[x],[y],[z],[w]]=z*[[−5],[−2],[1],[0]]

Final Answer

[[x],[y],[z],[w]]=z*[[−5],[−2],[1],[0]]

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