Write as a Vector Equality x+y+z=53 , x-y-z=-3 , 2y-x=-11

Problem

{[x+y+z=53],[x−y−z=−3],[2*y−x=−11])

Solution

1. Rearrange the equations so that all variables x y and z are in the same order and aligned.

x+y+z=53

x−y−z=−3

−x+2*y+0*z=−11

2. Identify the coefficients of each variable to form the coefficient matrix A

A=[[1,1,1],[1,−1,−1],[−1,2,0]]

3. Define the variable vector x and the constant vector b

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

b=[[53],[−3],[−11]]

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

[[1,1,1],[1,−1,−1],[−1,2,0]]*[[x],[y],[z]]=[[53],[−3],[−11]]

Final Answer

[[1,1,1],[1,−1,−1],[−1,2,0]]*[[x],[y],[z]]=[[53],[−3],[−11]]

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