Some help on a matrix question please.

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Discussion Overview

The discussion revolves around solving a matrix-related problem, specifically focusing on the interpretation of matrix operations such as transposition and inversion, as well as solving a system of equations represented in matrix form. Participants seek clarification on specific steps and calculations involved in these processes.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant expresses confusion about the meaning of \( A^T B \) and requests a step-by-step explanation.
  • Another participant mentions they have solved the equations by filling in zeros where variables do not exist, seeking confirmation of their results.
  • There is a clarification that \( A^T \) denotes the transpose of matrix \( A \).
  • A participant notes a calculation error when trying to compute a specific value using matrix inversion, leading to a discrepancy in expected results.
  • One participant points out a potential error in the calculation of a matrix element, suggesting that the middle number in \( A^{-1} \) is \( 0.75 \) instead of \( 0.375 \).

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the correctness of the calculations, as there are conflicting results and ongoing requests for verification of answers.

Contextual Notes

Participants express uncertainty regarding the steps involved in matrix inversion and the implications of filling in zeros in the matrix. There are unresolved calculations that may affect the overall understanding of the problem.

khehrap
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Hi. I am wondering if I can get some help on one or two questions on the sheet attached. I have worked out A^2B but am a bit puzzled on the meaning of A^TB. It is probably something very simple but I am struggling could someone help me possibly by listing out steps?.

Also I have worked out A^-1 but am stuck on solving the system of equations. As I though that you have to work out the inverse of a matrix when doing it for equations (AX=B format). although when I work out A ((2,-1)(3,2)(5,3) it is a 3x2 matrix therefore I am unable to get an inverse. Although the numbers are the same as the A^-1 question but just missing 0's therefore I think it may be something to do with that. Could someone help me please.

Thanks
Prab
 

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Hi I think I may have solved the equations (entering 0s where p1 p2 or p3 do not exist in the equation)

Could someone please still help to see if I have done it correct.
 
khehrap said:
I have worked out A^2B but am a bit puzzled on the meaning of A^TB.
$A^T$ denotes the transpose of $A$.

khehrap said:
Hi I think I may have solved the equations (entering 0s where p1 p2 or p3 do not exist in the equation)
Yes, in problem 2, the matrix of the system of equations is $A$.

khehrap said:
Could someone please still help to see if I have done it correct.
Please post your results so that we can check.
 
Evgeny.Makarov said:
$A^T$ denotes the transpose of $A$.

Yes, in problem 2, the matrix of the system of equations is $A$.

Please post your results so that we can check.

Hi Evgeny
I ralised that filling in the 0's gives me a matrix that I can use. Although I had already worked out the A^-1 in the first part of the question. therefore working row by row as normal.
The only problem I am facing (must be a calculation error - been doing this assignment for a while :)) is that when I try to work out p2 using matrix inversion shown below:

[1.250 x 2] + [0.375 x 16] + [-0.500 x 21] I am getting -4 not +4. Whereas the answer is +4 (calculation works correctly for both p1 and p3 giving me 3 and 2 respectively.)

I am using the figures above as a-1 gives the figures stated.

I have answered the cramers part too and been given the results 3 4 and 2 for p1 p2 p3.

Thanks
 
khehrap said:
[1.250 x 2] + [0.375 x 16] + [-0.500 x 21] I am getting -4 not +4.
The middle number in $A^{-1}$ is $6/8=0.75$, not 0.375. See WolframAlpha.
 

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