SOLUTION: Is the following a linear transformation from R3 to R3: L(x1,x2,x3) = (x3, x1+2x2-5x3, x1-x2) ? ok so i've worked on this a while, and i'm wondering: is it correct to show tha

Question 18984: Is the following a linear transformation from R3 to R3:
L(x1,x2,x3) = (x3, x1+2x2-5x3, x1-x2) ?
ok so i've worked on this a while, and i'm wondering: is it correct to show that the formulas

is closed under scalar multiplication and addition? and if it is, does that mean that the answer is yes? thank you so much for your help!
Answer by khwang(438) (Show Source): You can put this solution on YOUR website!
L(x1,x2,x3) = (x3, x1+2x2-5x3, x1-x2) ?
(FORGET yur wrong idea.)
It is linear, just try to check the linearity directly:

L(a(x1,x2,x3)+b(y1,y2,y3)) = a L(x1,x2,x3) + b L(y1,y2,y3)

Kenny

RELATED QUESTIONS
Determine whether the transformation T : R3 → R2 is a linear transformation. 􏰂... (answered by ikleyn)

Exercise 9 Determine whether the transformation T : R3 → R2 is a linear transformation. (answered by ikleyn)

Let u={(x1,x2,x3)in R3|x1+x2+x3=a} for a in R3 fixed. Show the u is a vector subspace if... (answered by venugopalramana)

is the following a linear transformation from R^3 to R^2? L(x1,x2,x3) = (x2-x3,x1+2) ? (answered by khwang)

Using matrix method evaluate X1 X2 X3 = 1 X1 2X2 X3 = 1 X1 2X2 X3 = (answered by Fombitz)

Hello, I would like to know if it's possible to calculate the equation... (answered by Alan3354)

Row echelon form of a system of linear equation is:

1   2  4  0  =  1
0   1... (answered by jim_thompson5910,Edwin McCravy)
(1) Write the following sets of linear equation in augumented matrix form and solve for... (answered by ikleyn)
(1) Write the following sets of linear equation in augumented matrix form and solve for... (answered by solver91311)