Write as a Vector Equality x+y=k , x-y=k

Problem

x+y=k,x−y=k

Solution

1. Identify the variables and constants in the system of linear equations. The variables are x and y and the constant on the right-hand side is k

2. Represent the coefficients of the variables as a matrix A The first equation 1*x+1*y=k gives the first row [1,1] and the second equation 1*x−1*y=k gives the second row [1,−1]

3. Define the vector of variables v and the vector of constants b

v=[[x],[y]]

b=[[k],[k]]

4. Construct the vector equality by multiplying the coefficient matrix by the variable vector and setting it equal to the constant vector.

[[1,1],[1,−1]]*[[x],[y]]=[[k],[k]]

5. Express the system as a linear combination of column vectors to show the vector equality form.

x*[[1],[1]]+y*[[1],[−1]]=[[k],[k]]

Final Answer

[[x+y],[x−y]]=[[k],[k]]

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