Which of the following DEs are first order linear DEs?

Q: vdor (2,1,3) be the {1,)1), (1, 2, >).(O, 1, 0)1 be the {ll,),l), (1, 2,3).CO,1, 0)) linear…

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Q: Express the following: as a linear combination of u = (2, 1, 4), v = (1, -1, 6) and w = (2, 2, 8).…

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Q: The linearization at a = 0 to v8 + 5x is A+ Bx. Compute A and B. A = B = ||

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Q: The linearization a at a = 0 to √8+7x is A + Br. Compute A and B. A B=

A: To Find: Linearization for fx=8+7x at a=0

Q: Consider the ODE system x' = A et + 3 with A = 4 1 3 a) Use the method of diagonalization to find…

A: Note: According to bartleby we have to answer only first question please upload the question…

Q: For A ∈ Mn(C) show that A = A1 + iA2 uniquely with A1 and A2 selfadjoint. Show that A is normal if…

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Q: Solve the following first-order linear DE's. y' + (cotx)y = xcscx, y = 1

A: we have to find the general solution

Q: Evaluate (2z + z – i) dz J|z-il=1

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Q: If la,} and {b„} are divergent then {a, + b,} is divergent. True False

A: Given: an and bn are divergent . The objective is to state whether an+bn is divergent is true or…

Q: 2. Given: PT || QS Prove: APRT O AQRS a. R. b. What similarity transformation maps APRT onto AQRS?

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Q: Y=√x, but is shifted to the right 1unit y =

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Q: find the Zero and order of the Linear trans formation TIRR defined as Teab)=la+bg d-byb)

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Q: det(A) Show that det(AB-') = %3D det(B)

A: Consider, Let A and B be the two n×n matrix, Now Consider, detAB-1 We know that the theorem, Let A…

Q: 3 For which value(s) of h is the set 4. -8 linearly 1 7 independent? Write your answer in one of the…

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Q: { (0,0,0), (3,5,6)} is linearly dependent in R' ulgn O ihi O

A: A set containing the zero vector (0,0,0) is linearly dependent.  Therefore the given set {(0,0,0),…

Q: The linearization at a = 0 to V6+ 5x is A+ Bx. Compute A and B %3D A = %3D B = %3D

A: Consider the given: Let fx=6+5x    at x=af0=6+50f0=6+0f0=6

Q: Find the Fourir for fcae) = (1+x) [-x, ] %3D

A: Given function is fx=1+x and −π,π We have to find the Fourier series of fx. The Fourier series of fx…

Q: { (0,3), (0,1) is linearly independent in R? ylgn O Ins

A: The given vectors are  (0, 3) and (0, 1) To find whether they are linearly dependent or not

Q: Determine whether the work done along the path C is positive, negative, or zero. zero O negative O…

A: We know,       work = ∫cF.dr               = ∫c∥F∥∥dr∥ cosθ    where θ is angle between F and drIf…

Q: verify that (A + B)T = AT + BT

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Q: { (0,0,0), (3,5,6)} is linearly dependent in R ulgn O ihi O

A: Solve the following

Q: Use the equations aF OF az ax az ay and ax OF ду OF az az az az and ax to find ду 5yz + 8x In(y) = =…

A: F=5yz+8xln(y)-z2∂F∂x=8ln(y), ∂F∂y=5z+8xy, ∂F∂z=5y-2z∂z∂x=8ln(y)5y-2z, ∂z∂y=5z+8xy5y-2z=5yz+8x5y2-2zy

Q: mple. Compute AB and BA where 1 -1 A = %3D B = -2 2 3 4

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Q: Prove that: sec a + sec(120° +a)sec(120° – a) = –3 sec 3a

A: To prove that  secα+sec(120∘+α)sec(120∘-α)=-3sec3α

Q: m is the mid point of AB find a Of AM

A: Equating the given relation gives the value of x . Then substituting the value of x in the…

Q: Show that the functions e*, cos x, and sin x are linearly independent using the Wronskian.

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Q: Find the of im < Re z< £ un der w-

A: Substitute w=u+iv and z=x+iy in the transformation. w=1zu+iv=1x+iyu+iv=x-iyx+iy.1x-iyu+iv=x-iyx2+y2…

Q: Which of the following points are collinear to (1,0) and (3,6)? Show graphically and analytically.…

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Q: Find ATA and AA". 2 0 1 %3D -1 4 2 (a) ATA 1 1 (b) AAT 21 Which of the products are symmetric?…

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Q: If Σa, is divergent and Eb, is divergent, then Z(a + b) is divergent.

A: The given statement is false as sum of two divergent series may converge. We illustrate this as…

Q: If xly, then show that ||x+ y|| = ||x- y|!.

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Q: Given: PT || QS a. Prove: APRTO AQRS R T. b. What similarity transformation maps APRT onto AQRS?

A: Corresponding angles are the angles that are formed when two parallel lines are interested by a…

Q: Which of these best describes T?

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Q: Calculate A and B so that t B %3D 1+1 (1-z²)

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Q: Consider the Simple Linear Model: 4 = Bo + Biz, + e, where i = 1,...,n, and e ~ IID(0, o?). Suppose…

A: Simple linear regression model: A simple linear regression model is given as y = b0 + bx, where y is…

Q: The linearization at a = 0 to √8+7e is A + Ba. Compute A and B. A B= || ||

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Q: - seyi + avīj + () dt = 3 3

A: We have to perform integration by parts and then insert given limit

Q: e vE dt 7laplare

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Q: Check the set 4 2 3 Mas(R) = 11 is linearly dependent or linearly independent

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Q: Qsit Prove that the Centre of a gp îs noymal. of

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Q: et §, ŋ, o be real numbers and consider ctors (1,5,§³); (1,ŋ,n³); (1,0,0²). Determine e conditions…

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Q: Solve the following Linear Homo, y" – 4y" – 5y' = 0 - %3D

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 3 and ajj = i. j. Th

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Q: 3. Determine whether the functions e and re are linearly independent or dependent by calculating…

A: f= {e^2x , x.e^2x} is Linearly independent if Wronskian is non zero.

Q: Let v = and v3 1 for which values of S, v,, V2 , and v3 are linearly %3D V2= %3D indonondont

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Q: Let T be. a linear trans formadion

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Q: Show that (t) =| 2 3t is the fundar

A: Given that,            y'=A(t)y                          ...(1) where                A(t)=-1t1-6t23t

Q: Show that (A − B)T = AT − BT .

A: We have to use the properties of subtraction of matrices and matrix transpose operation. In matrix…