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rsst123
 one year ago
If A,B,C,D are all invertible nxn matrices,solve for B
AB^1=D?
I understand to solve for C you need to multiply each side with the inverse, but I dont understand the premultiply and postmultiply rules
rsst123
 one year ago
If A,B,C,D are all invertible nxn matrices,solve for B AB^1=D? I understand to solve for C you need to multiply each side with the inverse, but I dont understand the premultiply and postmultiply rules

This Question is Closed

rsst123
 one year ago
Best ResponseYou've already chosen the best response.1Sorry i typed that wrong its AB^1C=D solve for B

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1Hello! :) in AB^1 C = D, you need to isolate B, right?? Also, do you understand that in Matrix algebra, AB and BA are different and not equal everytime?

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1lets take a simpler problem XY = Z isolate Y you would pre multiply by X or post multiply by X?

rsst123
 one year ago
Best ResponseYou've already chosen the best response.1you would multiply each side with X^1 correct?

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1yes, i meant X^1 sorry, pre multiply or post multiply?

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1if you had post multiplied it, XYX^1 = Z X^1 you could not have combined X and X^1 to get I (the Identity matrix)

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1now lets go to our problem, AB^1 C = D pre multiply by C or post? :)

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1yes! do it, and post some steps?

rsst123
 one year ago
Best ResponseYou've already chosen the best response.1AB^1CC^1=DC^1 A^1AB^1=A^1DC^1 I get to B^1=A^1DC^1 but im not sure what i should do from here

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1very good! you solved more than half of it! now take inverse on both sides...

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1and use this recursively, \(\large (PQ)^{1} = Q^{1}P^{1}\)

rsst123
 one year ago
Best ResponseYou've already chosen the best response.1perfect so the answer would be B=D^1CA ?

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1\([A^{1}D C^{1}]^{1} = (C^{1})^{1} D^{1} (A^{1})^{1} = CD^{1}A \)

rsst123
 one year ago
Best ResponseYou've already chosen the best response.1oh sorry my bad I was looking at the wrong work I was doing before this is my first time using this site and it's very helpful thank you for your help!!

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1hey, most welcome ^_^ happy to help :) feel free to message me if you wanna ask anything about this site :) \(\Huge \mathcal{\text{Welcome To OpenStudy}\ddot\smile} \)
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