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Given that T is a linear transformation, derive a formula for T.
 one year ago
 one year ago
Given that T is a linear transformation, derive a formula for T.
 one year ago
 one year ago

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brinetheryBest ResponseYou've already chosen the best response.1
Joe, if you have to go, I will understand :).
 one year ago

joemath314159Best ResponseYou've already chosen the best response.2
I need to think about this a little lol. I can see a way to solve the problem, but there might be a shorter way.
 one year ago

brinetheryBest ResponseYou've already chosen the best response.1
I just don't get how to solve these ridiculously hard questions. I would rather be doing diffEq than this!
 one year ago

joemath314159Best ResponseYou've already chosen the best response.2
First, do you notice that the vectors (1,0,1), (1,1,0), and (0,1,1) are linearly independent and form a basis?
 one year ago

joemath314159Best ResponseYou've already chosen the best response.2
Good, thats whats going to make this easy. Im going to type out the idea and post it, one sec.
 one year ago

joemath314159Best ResponseYou've already chosen the best response.2
oops oops oops, i was typing too fast. I dont mean the columns of A are linear independent, i meant the columns of that matrix next to A.
 one year ago

brinetheryBest ResponseYou've already chosen the best response.1
Oh my gosh, why did I not think of that?! I should've known to invert that sucker!
 one year ago

joemath314159Best ResponseYou've already chosen the best response.2
Here is the correction.
 one year ago

brinetheryBest ResponseYou've already chosen the best response.1
You're a much better explainer than the book is!
 one year ago

joemath314159Best ResponseYou've already chosen the best response.2
i have to run. Im sure there is probably a shorter or more interesting solution. anyways, have a good day :)
 one year ago

brinetheryBest ResponseYou've already chosen the best response.1
Thanks you SO much, I really mean it.
 one year ago

imranmeah91Best ResponseYou've already chosen the best response.0
I passed linear algebra because of joe
 one year ago

anonymoustwo44Best ResponseYou've already chosen the best response.0
ok so since we have a linear transformation, we then have an induced matrix A such that T(x)=Ax now since our output is an 2x1 matrix and that the vector x we input is an 3x1 matrix, then our induced matrix A is just a 2x3 matrix cause multiplying a 2x3 matrix with a 3x1 matrix will give us an output of 2x1 matrix. So if we find this matrix A, we could now find a formula :D. ok so let our matrix A be: \[A=\left[\begin{matrix}a & b & c\\ d & e & f\end{matrix}\right]\] now we'll get:
 one year ago

anonymoustwo44Best ResponseYou've already chosen the best response.0
I just wrote the solution :)) its hard to type lots of matrices
 one year ago

brinetheryBest ResponseYou've already chosen the best response.1
Thank you very much for your solution. But might I ask why you didn't want to just take the inverse since the 3 vectors form a basis?
 one year ago

anonymoustwo44Best ResponseYou've already chosen the best response.0
because I won't get the induced matrix or any formula for T from that :D which means I won't get any answer from that
 one year ago

anonymoustwo44Best ResponseYou've already chosen the best response.0
anyways goodluck with linear algebra which is used in differential equations also and has lots of implications on engineering, physics, economics, biology, chemistry, and math itself.
 one year ago

brinetheryBest ResponseYou've already chosen the best response.1
I did the inverse on both sides and came up with the same answer as what you got. I think it's easy to find the formula if one of the matrices is square. If one of them is not square, then we use the longer method, which is doing an induced matrix and solving for af. Thank you for showing me the other way so that I can use this method for nonsquare matrices.
 one year ago
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