Write as a Vector Equality 2x-3y=12 , 2x-y-z=4 , y+2z=6

Problem

{[2*x−3*y=12],[2*x−y−z=4],[y+2*z=6])

Solution

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

2. Align the equations so that each variable occupies a consistent column, including zero coefficients where a variable is missing.

2*x−3*y+0*z=12

2*x−1*y−1*z=4

0*x+1*y+2*z=6

3. Extract the coefficients into a matrix A the variables into a vector x and the constants into a vector b

4. Formulate the vector equality by expressing the system as a linear combination of constant vectors scaled by the variables.

Final Answer

x*[[2],[2],[0]]+y*[[−3],[−1],[1]]+z*[[0],[−1],[2]]=[[12],[4],[6]]

Want more problems? Check here!