Write as a Vector Equality 2x+4y-2z=0 , 3x+5y=1

Problem

2*x+4*y−2*z=0,3*x+5*y=1

Solution

1. Identify the variables and constants in the system of linear equations. The variables are x y and z

2. Rewrite the equations to ensure all variables are represented in both equations, using zero coefficients where necessary.

2*x+4*y−2*z=0

3*x+5*y+0*z=1

3. Separate the coefficients of each variable into distinct column vectors.

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

4. Express the system as a single vector equality where the linear combination of the column vectors equals the vector of constants.

Final Answer

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

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