Write as a Vector Equality x+y+5z=-6 , 3x+3y-z=10 , x+3y+2z=5

Problem

{[x+y+5*z=−6],[3*x+3*y−z=10],[x+3*y+2*z=5])

Solution

1. Identify the coefficients of the variables x y and z in each equation to form the column vectors.

2. Extract the x coefficients from the system to create the first vector:

x*[[1],[3],[1]]

3. Extract the y coefficients from the system to create the second vector:

y*[[1],[3],[3]]

4. Extract the z coefficients from the system to create the third vector:

z*[[5],[−1],[2]]

5. Set the linear combination of these vectors equal to the vector of constants from the right side of the equations.

Final Answer

x*[[1],[3],[1]]+y*[[1],[3],[3]]+z*[[5],[−1],[2]]=[[−6],[10],[5]]

Want more problems? Check here!