# Ok i got to the end of this whole Im theory but

• transgalactic
In summary, the conversation is about finding the kernel and image of linear transformations using a specific method. The first problem discussed involves finding the kernel of a transformation from R4 to R2, which is easily solved by finding the image of the transformation and using the basis vectors to find the kernel. The second problem involves finding the image of a transformation from R3 to R2, which is done by row reducing an augmented matrix. There is some confusion about which transformation is the correct one to use, but the process for finding the image remains the same. The conversation also touches on the concept of transposition and the importance of knowing when to stop the row reduction process and start using the A*(x, y, z) method.
transgalactic
ok i got to the end of this whole I am theory but...

i have two cases that i need guidense

in the link i showed a basic case and how we solve it using this method

http://img145.imageshack.us/my.php?image=img8275vc2.jpg

than i presented the first case that i can't solve
i which i tried to copy a case that we have delt with before
(with the b2=0)

than i presented the second case that i can't solve like our (b2=0) example

basicly may method say to make A*x=b

then to find the "b"s value for which we get a solution for the matrix

in the end we copy the "b" column with the conclution the gives us an answer for the matrix.

in both cases i get to part of the conclution but i can't go further
to wright down the "b" column with this conclutions and to
exract the vectors of the basis

?

(by the way)
i am using this method because i was tought that it works for every basis
unlike the tangugation mathod that works only for standart basis

Last edited:
How many different problems do you have here?

The first appears to be "Find the kernel of linear transformation A where A is the matrix
$$\left[\begin{array}{cccc} 1 & 0 & 0 & -3 \\ 2 & 0 & 4 & -5 \end{array}\right]$$.
from R4 to R2. It is easy to see that, multiplied by $<x_1, x_2, x_3, x_4>$ gives <x_1- 3x_4, 2x_1+ 4x_3- 5x_4>[/itex] it is equally easy to see that, for arbitrary $x_1, x_2, x_3, x_4$ those can give any numbers. The image of A is all of R2 and so < 1, 0> and <0, 1> are basis vectors. The rest of what you have there, I simply don't understand. And I have no idea what "tangugation" means! Translate please.

all of my questions are about finding the Im

i have there two cases that i don't know how to find their Im

i also tried to solve them using your method
but i have troubles with it

http://img167.imageshack.us/my.php?image=img8276dz3.jpg

and tangugation i think its the operation of transforming column into rows

i don't have a problem with the first metrix
i just showed an example of how this method is working
the problem is with the second metrix and the last metrix
in the middle i gave another example of how to find the I am
using this method

Last edited:
Your first operator changes the general (x, y, z, t) into (0, -y+ z, 0, 0). Isn't it obvious, that we can pick y and z to make -y+ z anything? (More technically, we can always solve -y+ z= a for any a- and it has an infinite number of solutions.) The image is simply the one dimensional subspace (0, a, 0, 0). You were almost there in writing y(0, -1, 0, 0)+ z(0, 1, 0, 0) since that is equal to (-y+ z)(0, 1, 0, 0). The image is the subspace having basis (0, 1, 0, 0) and, of course, is one-dimensional.

But you say the answer in your book is (0, 1, -1, 0). I don't know how they got that. The "augmented" matrix you show
$$\left(\begin{array} {ccccc}0 & 0 & 0 & 0 & 0 \\ 0 & -1 & 1 & 0 & b_2 \\ 0 & 0 & 0 & 0 & b_3+ b_2 \\ 0 & 0 & 0 & 0 & 0 \end{array}\right)$$
Looks like it is the result of row reducing another augmented matrix: it looks like it started as
$$\left(\begin{array}{ccccc} 0 & 0 & 0 & 0 & 0 \\ 0 & -1 & 1 & 0 & b_2 \\ 0 & 1 & -1 & 0 & b_3 \\ 0 & 0 & 0 & 0 & 0 \end{array}\right)$$
In other words, that the original transformation "mapped" (x, y, z, t) to (0, -y+ z, y- z, 0). If that is the case,since y- z= -(-y+ z) and, again, for y and z arbitrary, y- z can be anything, that is of the form (0, a, -a, 0)= a(0, 1, -1, 0) and, in this case, the image is the subspace having basis {(0, 1, -1, 0)}.

So which is, in fact, the correct transformation? (x, y, z, t)-> (0, -y+ z, 0, 0) which is what you give initially, or (x, y, z, t)-> (0, -y+ z, y- z, 0) which is what your book seems to be working with.

For the second problem where T(x, y, z)= (2x- y- z, -y+ z, 0), since 2x-y-z and y- z are arbitrary (there exist at least one solution to 2x- y- z= a and y-z= b for all a and b), any vector in the image if of the form (a, b, 0)= a(1, 0, 0)+ b(0, 1, 0). The image has basis {(1, 0, 0), (0, 1, 0)}.

Swapping rows and columns, in English, at least, is "transposition". What by, the way, is your native language? Your English is excellent.

Last edited by a moderator:
the only problem that remains for me is
"when to start this process?"

of making A*(x,y,z)

in any general problem i get a metrix like

(a b c)
(d e f)
(s t y)

from substituting A(e1) A(e2) A(e3) into the general formula

than i try to transform it so it will contain as much zeros as possible

(a b c)
(0 e f)
(0 0 y)

it can take several operations of row reduction for me to get to this resolt
i can go further and make this metrix to look like this

(a b 0)
(0 e 0)
(0 0 y)

i got the impression that we can get many I am resolts
because our matrix can change many time.
for example when you worked with
0 0 0 0
0-1 1 0
0 0 0 0

so you took the previos form of this matrix (one step before)
and then you made A*(x,y,z) and then you got the right answer

what is the guide line for me to know
for stopping row reduction procces and starting with A*(x,y,z) process
thanks?

Last edited:

## What is the "Im theory"?

The "Im theory" refers to the idea that consciousness and the self are an illusion created by the brain, proposed by philosopher Daniel Dennett.

## What does it mean to reach the end of the "Im theory"?

Reaching the end of the "Im theory" means understanding and accepting the concept that the self and consciousness are not separate entities, but rather products of brain processes.

## Is the "Im theory" widely accepted in the scientific community?

The "Im theory" is a controversial topic and is not universally accepted in the scientific community. Some scientists and philosophers support it, while others argue against it.

## How does the "Im theory" impact our understanding of the human experience?

The "Im theory" challenges traditional notions of the self and consciousness, and may lead to a reevaluation of how we perceive and experience the world around us.

## Can the "Im theory" be proven or disproven?

As a theory, the "Im theory" cannot be definitively proven or disproven, but it can be supported or refuted by evidence and further research.

• Calculus and Beyond Homework Help
Replies
2
Views
768
• Calculus and Beyond Homework Help
Replies
5
Views
1K
• Quantum Physics
Replies
3
Views
234
• Linear and Abstract Algebra
Replies
12
Views
1K
• Calculus and Beyond Homework Help
Replies
3
Views
2K
• Linear and Abstract Algebra
Replies
1
Views
126
• Calculus and Beyond Homework Help
Replies
4
Views
3K
• Calculus and Beyond Homework Help
Replies
26
Views
7K
• Differential Equations
Replies
3
Views
2K
• Calculus and Beyond Homework Help
Replies
9
Views
1K