Determine whether t : r^2 --> r^2,t((x. y)) = (x, y^2) is a linear transformation

 No, the given transformation T is NOT a linear transformation.

Step-by-step explanation:  We are given to determine whether the following transformation T : R² --> R² is a linear transformation or not :

We know that

a transformation T from a vector space U to vector space V is a linear transformation if for ∈U and a, b ∈ R

So, for (x, y), (x', y') ∈ R², and a, b ∈ R, we have

and

Therefore, we get

Thus, the given transformation T is NOT a linear transformation.

x = -3

y = -18

step-by-step explanation:

to solve by substitution, substitute one variable and solve for the other. then substitute again to find the remaining variable.

x-1/3(3x-9) = -3 since y=3x-9 substittute y.

x-1/3(3x-9)=-3

x + x +3 = -3

2x+3=-3

2x+3-3= -3-3

2x=-6

x=-3

substitute again into y=3x-9

y=3(-3)-9

y=-9-9

y=-18

can you rephrase the question ? it is unclear : -)

step-by-step explanation: