The discussion focuses on inverting a specific 2x2 matrix defined by the elements (-2e^2t)(sin(4t)), (-2e^4t)(cos(4t)), (-2e^2t)(cos(4t)), and (2e^4t)(sin(4t)). Participants emphasize using the formula A(INVERSE) = (1/ad-bc)(d, -b, -c, a) to compute the inverse. Key calculations involve determining the products ad and bc, specifically calculating (-2e^{2t}\sin(4t))*(2e^{4t}\sin(4t)) to find ad, resulting in -4e^{6t}\sin^2(4t). The discussion concludes with a successful simplification of the matrix inversion process.
PREREQUISITESStudents studying linear algebra, mathematicians working with matrix operations, and anyone needing to apply matrix inversion in practical scenarios such as engineering or physics.
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.
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.
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?
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.