Write as a Vector Equality (x+y+z)=2 , (2x+y-z)=-1 , (5-2z)=x

Problem

{[x+y+z=2],[2*x+y−z=−1],[5−2*z=x])

Solution

1. Rearrange the third equation into standard form a*x+b*y+c*z=d by moving the variable x and the constant 5

x+0*y+2*z=5

2. Identify the coefficients of the variables x y and z from each equation to form the coefficient matrix A

A=[[1,1,1],[2,1,−1],[1,0,2]]

3. Define the vector of variables x and the vector of constants b from the right-hand side of the equations.

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

b=[[2],[−1],[5]]

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

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

Final Answer

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

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