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How to invert this 2x2 Matrix?

ends

New member
Sep 28, 2013
9
(-2e^2t)(sin(4t)) , (-2e^4t)(cos(4t))

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

Please and Thank you!!
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
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

New member
Sep 28, 2013
9
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.
 

Jameson

Administrator
Staff member
Jan 26, 2012
4,052
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?
 

ends

New member
Sep 28, 2013
9
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.
 

Jameson

Administrator
Staff member
Jan 26, 2012
4,052
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.
 

ends

New member
Sep 28, 2013
9
Thanks guys...it simplified nicely, really appreciated the help, cheers.