Given the linear transformation ( T:mathbb{R}^2 rightarrow mathbb{R}^2 ) defined by ( T(x, y) = (2x+y, x+3y) ). Find the pre-image of the point (5, 11) under the transformation T.

Question

Accepted Answer

Step:1 ：First, set the image of T equal to the given point (5, 11), which gives us the system of equations: [ begin{cases} 2x+y = 5  x+3y = 11 end{cases} ]Step:2 ：Next, solve the system of equations. Multiply the second equation by 2 and subtract the first equation from the result to eliminate x. This gives us: [ 2x+6y-2x-y = 22-5 implies 5y = 17 implies y = frac{17}{5} ]Step:3 ：Substitute (y = frac{17}{5}) into the first equation to solve for x: [2x + frac{17}{5} = 5 implies 2x = frac{8}{5} implies x = frac{4}{5} ]

Answer

Step: 1 ：First, set the image of T equal to the given point (5, 11), which gives us the system of equations: [ begin{cases} 2x+y = 5  x+3y = 11 end{cases} ]Step: 2 ：Next, solve the system of equations. Multiply the second equation by 2 and subtract the first equation from the result to eliminate x. This gives us: [ 2x+6y-2x-y = 22-5 implies 5y = 17 implies y = frac{17}{5} ]Step: 3 ：Substitute (y = frac{17}{5}) into the first equation to solve for x: [2x + frac{17}{5} = 5 implies 2x = frac{8}{5} implies x = frac{4}{5} ]

Given the linear transformation $T : R^{2} \to R^{2}$ defined by $T (x, y) = (2 x + y, x + 3 y)$ . Find the pre-image of the point (5, 11) under the transformation T.

Answer

Popular Problems

Given the linear transformation T:R2→R2 defined by T(x,y)=(2x+y,x+3y). Find the pre-image of the point (5, 11) under the transformation T.

Answer

Popular Problems

Given the linear transformation $T : R^{2} \to R^{2}$ defined by $T (x, y) = (2 x + y, x + 3 y)$ . Find the pre-image of the point (5, 11) under the transformation T.