Sure! Here is the transcription of the text for an educational website:---**3. Let**\[A = \begin{bmatrix}3 & 3 & 0 & 5 \\2 & 2 & 0 & -2 \\0 & 1 & -3 & 0 \\2 & 10 & 3 & 2\end{bmatrix}.\]**Evaluate det(A) by a cofactor expansion along a row or column of your choice. Is A invertible?**---

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Answered: 3. Let A - 3202 3219 3 3 0 5 0 -2 -3 0…

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 #1: Let V be the set of all ordered pairs of real numbers (µ₁, 42) with u₂ > 0. Consider the following addition and scalar multiplication operations on u = = (u₁, u₂) and v = (V₁, V2): u + v = (u₁ + v₁ + 4,7u2v2), ku = (ku1, ku2) Use the above operations for the following parts. (a) Compute u + v for u = (-2,3) and v = = (-2,2). (b) If the set V satisfies Axiom 4 of a vector space (the existence of a zero vector), what would be the zero vector? (c) If u = (5,5), what would be the negative of the vector u referred to in Axiom 5 of a vector space? (Don't forget to use your answer to part (b) here!)
Example:3 Verify Cayley-Hamilton theorem, and find A-1 [2 A=0 1 [1 1 2.
Q#03 Let A= 3. (a) Compute det (A) using a cofactor expansion along row 2. (b) Find A adj(A). (c) Find det (2A-'adj(A)).
3) Determine the inverse lapley transform of 105² +42s + 24 F(s) 53 + 45² +35
Example 19-5. Use the method of separation of symbols to prove the following identities : (a) Uo + U1 + ... + U, = ( "i') Uo +( "2') auo +(") a²u, + .. n + 1 n + N + 1 3 + ( *:) a" n + 1 (b) Uz x + Uz x² + Uz x³ + .. x² %3D (1– x) U1 + (1 – x)2AU1 + (1 – x)34²U¡ + .. |
If NG and both G and G/N are soluble, show that G is soluble.
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3. Let A - 3202 3219 3 3 0 5 0 -2 -3 0 2 10 3 2 Evaluate det(A) by a cofactor expansion along a row or column of your choice. Is A invertible?