Write as a Vector Equality x+2y=3 , 2x+ky=2

Problem

{[x+2*y=3],[2*x+k*y=2])

Solution

1. Identify the coefficients of the variables x and y on the left side of the system of equations.

2. Construct the coefficient matrix A using the values 1 2 2 and k

A=[[1,2],[2,k]]

3. Define the variable vector x and the constant vector b from the right side of the equations.

x=[[x],[y]]

b=[[3],[2]]

4. Express the system as a single vector equality in the form A*x=b

[[1,2],[2,k]]*[[x],[y]]=[[3],[2]]

5. Alternatively, write the system as a linear combination of column vectors.

x*[[1],[2]]+y*[[2],[k]]=[[3],[2]]

Final Answer

[[1,2],[2,k]]*[[x],[y]]=[[3],[2]]

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