If A has rank r, then it has r x r submatrix S that is .a Singular Invertible .C NES TEAM O Skew-Symmetric Symmetric

Q: If A is invertable then A is diagonalizable. Select one: O True O False

A: If a matrix A of order nxn is invertiable then it has n disctinct eigen values.  And corresponding…

Q: Consider the vector space V and the constant keR. verify that the expansion / contraction T: V → V,…

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Q: ® Find the_functian that satisfies the following conditions for some constant Eceficients c,and c…

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Q: Give V = C([0, 1]) the inner product defined as follows: (f, g) :| f(t)g(t) dt for all f, g e V.…

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Q: 6. If Z is the ocentroid of AWXY, WR = 87, SY = 39, and YT 48, find each missing measure. W a) WS =…

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Q: The Poisson kernel Pr (0 – p) on the unit disk is given by 1-r2 1–2r cos(0-4)+r² O Enez r" sin (n (0…

A: Let f(z) be analytic inside the unit disk. then if

Q: 7. Use the Divergence Theorem step by step including sketch of the solid shape to find the flux f SF…

A: sketch of the solid shape is as follows

Q: Find a norm of the operator A(x) = o (s4 + s? )x(t)dt in space C[0, 1]. a. 4 Ob. O c. 2 4 O d. 15 1…

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Q: Let M be an elliptic paraboloid z = y² + 2?. (A) "Compute the Gauss map and the shape operator. (B)…

A: Answer for sub question a: Given x=y2+z2 A parametrization is given by: Xu,v=u2+v2,u,v Then,…

Q: Compute the Wronskian of the following equation. y" – 4y' + 4y = xe2x %3D

A: Given: y''-4y'+4y = xe2x

Q: Theorem 16. Show that if t: V→ V is a self duct space V, then s* is is self-adjoint for every lin…

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Q: Find a relating ab and c Sothat the linear Systen X +2y- 2X +3 y +3Z = 6 5X +9y - 6Z = c eojarrar A…

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Q: Given that vec F =x^ 2 y hat i -(z^ 3 -3x) hat j +4y^ 2 hat k find the k- component of ( nabla* vec…

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Q: Let yk = k² and Zk = 2k|k|. Are the signals {yk } and {Zk } inearly independent? Evaluate the…

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Q: . Solve the following Dirichlet problem on a disk V²U(r,0) = 0, 0<r<1, -asosa U(1,0) = 0, - <o< T.

A: This question based on Dirichlet problem on a disk from partial differential equation.

Q: Let Ps have the inner product given by evaluation at-2,-1, 0,1, and 2. Let p(t) = t2- 2t and q(t) =…

A: Let P3 have the inner product given by evaluation at -2, -1, 0, 1 and 2 . Let p(t) = t2-2t  and q(t)…

Q: 3. Calculate the circulation of A=p coso ap+ z sino a: around the edge L of the wedge defined by 0≤p…

A: Here we have given that, A=ρcosϕaρ+zsinϕaz and wedge is defined as, 0≤ρ≤2, 0°⩽ϕ≤60° and z=0 as shown…

Q: Consider the D-operator P(D) = mD² + 2kD +¢, where m and c are positive. If -c/m < k< 0, then

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Q: In AKLM, R is the centroid. If RQ=10 find LQ. L N P R K M

A: In ∆KLM The centroid of a triangle is "R". The length of the RQ=10. The objective is to find the…

Q: A S O Consi der Hhe folhning {(01), (-1,)}, B = [x]e - [;] %3D O find the fransi tion matria from B…

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Q: In AEFG, L is the centroid. If LJ=9 find EL. H J E K

A: We have given a triangle. In which LJ is the centroid. And we have to find EL

Q: (a) If ker(L) has dimension s, what is the rank of L? (b) If ker(L) # {0v}, show that L is not…

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Q: Let M be an elliptic paraboloid a = y? + z². Compute the Gauss map and the shape operator. Find k…

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Q: 2) Determine the dimension of Null A and Col A for the marix [1 2 3 0 0 A =|0 0 1 0 1 0 0 0 1 0

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Q: Find the norm of (-4,- 1/4,3, 1/3) belong to R^4 w.r.t the Euclidean Inner Product on R^4.

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Q: The inverse image of the disk | z |< under T(z)=is z+1

A: Given: Disk z&lt;12. To find: Inverse image of disk under Tz=zz+1.

Q: Z is the centrold of AUVW. W What is ZX if WZ = x? A. 5 O B. В. ос. 2т O D.

A: Answer is mentioned below

Q: Let M be an elliptic paraboloid r =; y² + 2?. Compute the Gauss map and the shape operator. Find k…

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Q: Evaluate the double integral // (3r - 7y)dA, where D is the domain bounded inside the tangle with…

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Q: The following PDE u + u = 0 O a. Homogeneous (on the x-y plane) Ob. Nonhomogeneous on the x-y plane,…

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Q: Consider f, g E T° (R") and 0 > 0. Show the following results on the subdifferential. (a) a(0f)(x) =…

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Q: 4. Show that the norm on l0 given by I| (11, .., In...) |lo= sup{|r;| : j= 1,2, ...} can not be…

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Q: Consider the following semilinear first-order PDE ди ди + Y = xe¯u ду (i) Find the general solution…

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Q: in the space R2 on the field R Prove that everyone M = {(x, y): x + 2y = 0} %3D %3D N = {(x,y): 5x +…

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Q: 22 y? 2 u?. Show that A is invertible if and r y 23 w3 3: Let A = only if r, y, z and w are…

A: Given that the matrix A=1111xyzwx2y2z2w2x3y3z3w3 Show that A is invertible if and only if x,y,z and…

Q: Q4 Let V=R, defined the addition by: %3D with slandard scalar multiplication. Is Va valtov space…

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Q: nozmal subgsoup H of ozder 4 of subquoup H of order 4 of Consieles dihedral poove that a Dy= Lasbi…

A: It is known that; Next, we show;

Q: ☺ RB=R defuid by T☺)- matria "A" it. T@)- A:). つレ- TV4 Let T: -3v-Jw ). Füd

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Q: Given an n xn-matriz A over a field K ry column vector b, there is a unique column v lution to Ar=0…

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Q: In AFGH, M is the centroid. If FM=20 find FK. G J K F H L

A: Given: In △FGH,  M is the centroid of the triangle. FM = 20

Q: Let T:R'R? Linear trans formation in the form T(X,4,Z) =(X+24,0,32) grand fatherokert ☺ Img 3.

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Q: Now Considex a fn abarce of set of finctrons f() x€ (-00gt00) such that of d del varieble Oes ox→ I…

A: As per the instruction, we will be answering only the second part. For (ii), We consider a function…

Q: Use Green's Theorem to evaluate S. axy dy + cxy dy, where C is a counterclockwise oriented…

A: Given : a=2, c=8 We have to use Green's Theorem to evaluate            ∫C axy dy+cxy dy where C is a…

Q: [0, 1]. If f(1), g () e V then show that (f(t), g (t)) = [ƒ(t) g (f) dt defines an inner product on…

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Q: Lee f() = n't3n"- 2x' + 2 %3D And glu) = x+ 2n+1 E Q (n) Find the unique polynomi als g (x), Y(x) E…

A: In the given question we have to find the q(x) and r(x) s.t f(x)=q(x)g(x)+r(x) where…

Q: 1 Let A= -2 . Show that A is positive semidefinite and find A2 4

A: Given the matrix is A=1-2-24. Show that A is positive semidefinite and find A12.

Q: Find of the operstor a norm A(x) = S (2.+st)x(t)dt %3D A: C [o,1] →L [o,I] O a. 2 O b. 7/12 O c.…

A: Option (c) is correct.

Q: The value of a' for which f : R → R, ax +7 flx) is invertible lies in %3D 2 x* +4 (а) (0, 2) (b) (1,…

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