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Problem 5. Define a function d: R²×² → R by show the following equalities: (i) for any scalar r ER, d ra ¹ ( [re $]) = r · d ([a d]) rc (ii) d (D) - - (1) [ ([:]) = -d d ([%]) - ad-be. bc, (iii) d(1₂) = 1 (iv) a ([a+u :)) = a([c &]) d ¹ ( [$]) + d

Problem 5. Define a function d: R²×² → R by show the following equalities: (i) for any scalar r ER, d ra ¹ ( [re $]) = r · d ([a d]) rc (ii) d (D) - - (1) [ ([:]) = -d d ([%]) - ad-be. bc, (iii) d(1₂) = 1 (iv) a ([a+u :)) = a([c &]) d ¹ ( [$]) + d

Advanced Engineering Mathematics
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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Problem 5. Define a function d: R²×2 → R by show the following equalities: ra (i) for any scalar r € R, d ¹ ( [re b]) = rc d (ii) d ([a b]) (iii) d(1₂) = 1 = -([]) -d a *([])= ad-bc, ([ª 9 n (iv) d ([a+u d]) = a([a b]) -d ([a b]) d =r.d (E ) -
Transcribed Image Text:Problem 5. Define a function d: R²×2 → R by show the following equalities: ra (i) for any scalar r € R, d ¹ ( [re b]) = rc d (ii) d ([a b]) (iii) d(1₂) = 1 = -([]) -d a *([])= ad-bc, ([ª 9 n (iv) d ([a+u d]) = a([a b]) -d ([a b]) d =r.d (E ) -
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