Consider the general 2 × 2 linear system. ax + by = u сх + dy = V Assume that a unique solution exists. Verify that du – bv av — си - ad - bc y = ad – bc 2 points for verifying x, 2 points for verifying y. (Hint: By "verify," I mean that I am giving you a solution and you have to show that it is correct. You can do this by deriving the solution, or you can do this by checking the solution directly. In this case, both methods take the same amount of work. You should choose whichever way feels better.)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the general 2 x 2 linear system.
+ by
cx + dy
ax
= U
= V
Assume that a unique solution exists. Verify that
du – bv
av
си
x =
ad – bc
ad – bc
2 points for verifying x, 2 points for verifying y.
(Hint: By "verify," I mean that I am giving you a solution and you have to show that it is
correct. You can do this by deriving the solution, or you can do this by checking the solution
directly. In this case, both methods take the same amount of work. You should choose
whichever way feels better.)
Transcribed Image Text:Consider the general 2 x 2 linear system. + by cx + dy ax = U = V Assume that a unique solution exists. Verify that du – bv av си x = ad – bc ad – bc 2 points for verifying x, 2 points for verifying y. (Hint: By "verify," I mean that I am giving you a solution and you have to show that it is correct. You can do this by deriving the solution, or you can do this by checking the solution directly. In this case, both methods take the same amount of work. You should choose whichever way feels better.)
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