Supose L:? 3 ?? 3 is a matrix transformation and L((?1,?2,2))=(1,2,?3) and L((?1
ID: 2964395 • Letter: S
Question
Supose L:?3??3 is a matrix transformation and L((?1,?2,2))=(1,2,?3) and L((?1,?1,1))=(?5,?3,?3).Evaluate the following. Enter 0 if there is not enough information given. Otherwise, write your answers as row vectors for this question.
1. L(3(?1,?2,2)?2(?1,?1,1))=
2. L((3,5,?5))=
3. L((?2,?6,6))=
4. L((1,3,?4))=
I got for
1. (13,12,-3) which is correct
2. can't figure out
3. can't figure out
4. 0 which is correct.
Can someone help me with #2 and #3 with shown work or an explanation please! Thank you
Explanation / Answer
2.
let
(3,5,-5) = a(-1,-2,2) +b(-1,-1,1)
=>
3 = -a-b,
5 = -2a-b
-5 = 2a+b
=>
a = -2, b = -1
=>
(3,5,-5) = -2(-1,-2,2) -(-1,-1,1)
=>
L(3,5,-5) = L(-2(-1,-2,2)) +L(-(-1,-1,1)) = -2L(-1,-2,2) -L(-1,-1,1) = -2(1,2,-3) -(-5,-3,-3) = (3,-1, 9)
3.
let
(-2,-6,6) = a(-1,-2,2) +b(-1,-1,1)
=>
-2 = -a-b,
-6 = -2a-b
6 = 2a+b
=>
a = 4, b = -2
=>
(-2,-6,6) = 4(-1,-2,2) -2(-1,-1,1)
=>
L(-2,-6,6) = L(4(-1,-2,2)) +L(-2(-1,-1,1)) = 4L(-1,-2,2) -2L(-1,-1,1) = 4(1,2,-3) -2(-5,-3,-3) = (14,14, -6)
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