Let T: R2 --> R2 be the linear transformation given by T(x,y)=(2x+y, x+y). Find T -1(x,y).

Question

Let T: R2 --> R2 be the linear transformation given by T(x,y)=(2x+y, x+y). Find T -1(x,y).
🧐 Not the exact question you are looking for?Go ask a question

Solution 1

To find the inverse of the transformation T, we need to solve the system of equations:

2x + y = u x + y = v

for x and y in terms of u and v.

First, subtract the second equation from the first to get:

x = u - v

Then, substitute x = u - v into the second equation to get:

u - v + y = v y = 2v - Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solv

This problem has been solved

Similar Questions

Let T: R2 --> R2 be the linear transformation given by T(x,y)=(2x+y, x+y). Find T -1(x,y).

Find a linear transformation 7: R2 R2 such that 7(1,-2) = (1, 1) and T(0, 1) = (2,3), where B = {(1,-2), (0, 1)) is a basis of IR2.

Does there exist a linear transformation T : R2 → R4 such that Range(T ) ={(x1, x2, x3, x4) : x1 + x2 + x3 + x4 = 0

Find the general solution of each of the equation if one solution is given (i) xy′′ + (2x + 1)y′ + (x + 1)y = 0, y1(x) = e −x

Which of the given function is linear?*f (x) = | 3x – 1|f(x) = 2/(x + 7)f(x) = √x - 4f(x) = 2x/3

1/3