How Do You Invert This 2x2 Matrix?

  • Context: MHB 
  • Thread starter Thread starter ends
  • Start date Start date
  • Tags Tags
    Matrix
Click For Summary

Discussion Overview

The discussion centers around inverting a specific 2x2 matrix that contains exponential and trigonometric functions. Participants explore the application of the inversion formula and seek clarification on handling complex expressions within the matrix.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant presents a 2x2 matrix with complex entries and requests assistance in inverting it.
  • Several participants ask for clarification on what the original poster has attempted to do, emphasizing the importance of understanding where they are stuck.
  • A formula for inverting a 2x2 matrix is introduced, but the original poster expresses uncertainty about applying it to the given matrix.
  • Another participant suggests calculating the products \(ad\) and \(bc\) as part of the inversion process and provides an example multiplication of terms from the matrix.
  • Further clarification is requested on how to multiply the complex terms, with a participant breaking down the multiplication into simpler components.
  • A participant confirms that the simplification of the terms was successful and expresses gratitude for the assistance received.

Areas of Agreement / Disagreement

Participants generally agree on the use of the matrix inversion formula, but there is uncertainty regarding its application to the specific complex terms in the matrix. The discussion remains unresolved regarding the complete inversion process.

Contextual Notes

Participants do not fully resolve the mathematical steps involved in applying the inversion formula to the complex matrix, and there are missing details about the assumptions made in the calculations.

ends
Messages
9
Reaction score
0
(-2e^2t)(sin(4t)) , (-2e^4t)(cos(4t))

(-2e^2t)(cos(4t)) , (2e^4t)(sin(4t))

Please and Thank you!
 
Physics news on Phys.org
Can you show us what you have tried? Our helpers will be better able to provide you with relevant help if they can see where you are stuck and/or where you may be making mistakes.
 
MarkFL said:
Can you show us what you have tried? Our helpers will be better able to provide you with relevant help if they can see where you are stuck and/or where you may be making mistakes.

So since it's a 2x2 matrix, it's easier to use the equation A(INVERSE) = (1/ad-bc)(d , -b
-c , a)

I get stuck here, I don't really know how to apply this formula when it's in a more complex form like this.
 
ends said:
So since it's a 2x2 matrix, it's easier to use the equation A(INVERSE) = (1/ad-bc)(d , -b
-c , a)

I get stuck here, I don't really know how to apply this formula when it's in a more complex form like this.

Hi ends!

I don't see why that formula wouldn't work here. Try calculating $ad$ and $bc$ first. What is $(-2e^{2t}\sin(4t))*(2e^{4t}\sin(4t))$ for example?
 
Jameson said:
Hi ends!

I don't see why that formula wouldn't work here. Try calculating $ad$ and $bc$ first. What is $(-2e^{2t}\sin(4t))*(2e^{4t}\sin(4t))$ for example?

Thank you, but can you equate this one for me so I have a general idea of how to multiply these two large terms? I'm not entirely sure how to go about it, and since it's my last chance to submit it online, I don't want to mess it up.
 
ends said:
Thank you, but can you equate this one for me so I have a general idea of how to multiply these two large terms? I'm not entirely sure how to go about it, and since it's my last chance to submit it online, I don't want to mess it up.

Multiply things that are alike. I think of each term as containing a regular number, an "e" expression and a trig term. So $(-2e^{2t}\sin(4t))*(2e^{4t}\sin(4t))=-4e^{6t}\sin^2(4t)$. So there's your $ad$. Try $bc$ and then try combining these two to simplify them somehow.
 
Thanks guys...it simplified nicely, really appreciated the help, cheers.
 

Similar threads

MHB Linear system of equations: Echelon form/Solutions
  • · Replies 3 ·
Replies
3
Views
1K
Differential Equations System Solutions
  • · Replies 9 ·
Replies
9
Views
2K
Graduate Solving Transition Matrix: Find Coefficients of B to B
  • · Replies 1 ·
Replies
1
Views
41K
Solve Convolution Shortcut for x(t)
  • · Replies 67 ·
3
Replies
67
Views
9K
Undergrad How can I solve this without using integrating factor?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Linear Transformations and matrix representation
  • · Replies 5 ·
Replies
5
Views
5K
Solving a System of Differential Equations with Complex Eigenvalues
  • · Replies 9 ·
Replies
9
Views
4K
MHB How can the Wronskian be used to determine linear independence?
  • · Replies 2 ·
Replies
2
Views
2K
MHB Integral of $\cos^4(t)$: Solution & Explanation
  • · Replies 8 ·
Replies
8
Views
2K
MHB How Do You Find the Curvature at (2, 4, -1)?
  • · Replies 2 ·
Replies
2
Views
3K