X1 X2-X1 Let L: R→R be a linear operator such that L X2 )= X3X2 , then Ker(L) spanned by: -> X3 X3-X1] Select one: a. b. с. (e, e2, e3) d.

Q: Q5. Are the set of vectors {[0 2 1]",[1 1 1]", [3 2 1]", [3 0 1]"} linearly independent? Does the…

A: Set of vectors are linearly independent if there is no non-zero solution of c1,c2,c3,c4. If there is…

Q: ) Consider the functions f(x) = (x + 3)² and g(x)=√x a.) Find fo g(9) 13 9(9) = √5 = 8(3) =(3+3) ²…

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Q: Example: Calculate the value of (@w/0x) at the point (x, y, z) = (2, -1,1) if:- w = x2 + y2 + z? z3…

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Q: 2.x - y-z = 0 5x - 2у +2: 3 Зх + у - 2: -8

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Q: 5|, B= -14|, and C = |2 2 -11 B and C linearly dependent, or are they linearly independent? -arly…

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Q: Show that (u×v)· w = u ·(v×w).

A: As we know that, Multiplication is an Associative Property, i.e. (a x b).c=a.(b x c) and Sometimes…

Q: ?w Əv у Find when u = 0, v=0 if w=x² + ₁ x=6u-2v + 1₁ y=u+4v - 1.

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Q: d The mapping is a linear operator. Is 2 a linear operator? Is c a linear operator? da de

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Q: Evaluate x² + 1 – Vx²2 – 1 dx - Va4 – 1 |

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Q: Let x 4 || - N and y = Find the vector v = 3x - 4y and its additive inverse. 18 [2] 4

A: The additive inverse of a vector v = <a , b> is  - v = <-a , -b>

Q: +タ x2 – 1

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Q: Use Cramer's rule find yhe solution of x1: 2x1+X2-3x3=0 4x1+5x2+X3=8 -2x1-x+4x3=2

A: write the matrix D from the given equations  D=21-3451-2-14 calculate the determinant D…

Q: дz дz \f z = f (x, y), find and for the following equation ?х ду z = (x2 + xy3)4

A: Let Using the chain rule, and

Q: e*, e2x, e3x А. О В. 2ебх С. 12е бх 6x D. 48eбx

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Q: Let i = (– 3, - 2, 3) and i = (1, – 6, – 7). Compute the following: i xü = i x ủ u X u =

A: Since you have asked a question with multiple parts in a single request, we would be answering only…

Q: Express in the form of x + iy: 6-7i (i) 5+i 1 + (3+i)2 1 (ii) (3-i)2

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Q: xyzx + 2y³ (Zyy) = 1 Dependent variable/s: Independent variable/s: Type: Order: Degree: Linearity:

A: Given: Here, the dependent variable is z, independent variables are x and y. And the type is a…

Q: дz дz If z = f(x, y), find a and for the following equation əx ду z = x² + 3xy + y³

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Q: 1 1 Let A = Find the values of a such that A is not diagonalizable 1 1 0 0 1

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Q: 2. In y = c+ C2*

A: We have to eliminate the arbitrary constants c1 and c2 from the equation lny=c1+c2x. This is…

Q: Cakulate (3i+2j+k) • (i + zj - k

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Q: Using the substitution u = (A) (B) C D 1+1 du [₁ -1/2 du [(u ¹/2 - u-1/2) d du (u - 1) / u-²1) x + 1…

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Q: Vxdx 2. For J T-Vx use 4 O u = JA u = x O u = Ja

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Q: 9 Give with an not example of T: W≤X →Y, to XT Ext. .R. boundedag. - keše bes

A: Please find the solution innext step this is an non-example of Tietze extension theorem in Topology.

Q: Which of the following operators in R'are linear? 1. T(x) = (8x2, -5x, -9x) %3D 2 T(x) = (10x; - 7x2…

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Q: Let x(bar) = (3,-5,2,1,-2) element of R5. Find the norm of x(bar) using the usual norm on R5

A: The norm of x is the distance between a point x to the origin.

Q: Consider the linear operator T: R? → R² defined by the following equations. w1 = 3x1 + 11x, W2 = X1…

A: we have to find the inverse of T          (i.eT-1(w1,w2))where T:R2→R2 is given by…

Q: Q7) True or False, and Justify your answer. If v1, v2, ... V4 are in Rª and v3 = 2v1 + v2, then…

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Q: -2u X = u +

A: to find the linear combination, draw a vector 4u and 4v

Q: Diagonalized  if possible, where is A=[■(4&0&1@1&1&0@3&0&1)].

A: Given A =   4 0 1     1 1 0     3 0 1