Find the General Expression for a Linear Transformation

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Discussion Overview

The discussion revolves around finding the general expression for a linear transformation represented by a matrix product. Participants explore how to compute the result of multiplying a given matrix by a vector, with a focus on understanding the transformation's output.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about how to approach the problem.
  • Another participant provides the matrix and vector involved in the transformation and suggests computing the matrix product.
  • A participant proposes a potential answer to the transformation but is unsure about the correctness of their expression.
  • A later reply confirms the matrix product calculation and presents the resulting vector, indicating agreement with the computed output.

Areas of Agreement / Disagreement

There is some agreement on the computed output of the matrix product, but initial confusion and uncertainty about the approach are present. The discussion does not fully resolve the understanding of the transformation process.

Contextual Notes

Participants demonstrate varying levels of familiarity with matrix notation and LaTeX, which may affect clarity in communication. There are unresolved aspects regarding the initial question and the method of arriving at the final expression.

Who May Find This Useful

Students learning about linear transformations, matrix operations, and those seeking assistance with homework problems in linear algebra.

Leanna
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View attachment 6275

I don't quite get this question, how is it done ?
 

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Hi Leanna,

It is asking you to compute the matrix product $$\begin{pmatrix}-1&-2&0&1\\0&3&1&1\\2&0&2&-4\\0&-1&0&0\end{pmatrix}\begin{pmatrix}r\\s\\t\\u\end{pmatrix}$$
 
Can you see if answer to first question is (-r, 3s, 2t, u)?

Or is it
Idk how to use latex but it's one matrix
(-r -2s+u)
(3s+t+u)
(2r+2t-4u)
(. -s. )
 
Leanna said:
Can you see if answer to first question is (-r, 3s, 2t, u)?

Or is it
Idk how to use latex but it's one matrix
(-r -2s+u)
(3s+t+u)
(2r+2t-4u)
(. -s. )

According to an online matrix calculator I found:

$$\left(\begin{array}{c}-1 & -2 & 0 & 1 \\ 0 & 3 & 1 & 1 \\ 2 & 0 & 2 & -4 \\ 0 & -1 & 0 & 0 \end{array}\right)\left(\begin{array}{c}r \\ s \\ t \\ u \end{array}\right)=\left(\begin{array}{c}-r-2s+u \\ 3s+t+u \\ 2r+2t-4u \\ -s \end{array}\right)\quad\checkmark$$
 
Thanks a lot
 

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