(6) Define T1,T2,T3 : R³ → R³ by T1 T3( y ) Y y – z (a) Find TT2( y). (b) Suppose that T1,T2, T|T2 are left multiplications by matrices A, B, C, respectively. Find A, B and C, and verify AB = C.

Q: Let u = (2,6, 4) and 7 = (-1, -2, - 7). Compute the following: ū. v = vu - ||||²

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

Q: 5. Determine the combination V x (Vf) given that X" + y"

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Q: Find (a) u × v, (b) v × u, and (c) v × v.…

A: Given : u =0,2,1v = 1,-3,4(a) u x v = ijk0211-34u x v =i 21-34    -j0114  +k021-3          = i(8+3)…

Q: 3 Let x = (9, −9, −4) and y = (-6, 6, -9) be in R³ and a be in R. Then ax + y = ( ,23).

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Q: Let →u=⟨6,−4,−6⟩ and →v=⟨−5,−3,−6⟩. Compute the following:

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Q: Give an example of C = diag(c1, C2, C3) and D = diag(dı, d2, d3) where Tr(C) det(D), but C is not…

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Q: (d) Develop an estimated regression equation for the data of the form ý = b, + b,x + b,x. (Round b,…

A: e) Consider the following table for necessary calculations. y x x2 12 22 484 22…

Q: Let ā= (2, 5, 7) and 6 = (1, 3, 4). (a - b) × (a + b) = X (3,16,33) X

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Q: Let u (9, 9, 8) and = (-9, -1, - 8). = Find proj, (u). -

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Q: Determine whether (p→q)→(q→r) is equivalent to q→r. Justifyyour claim.

A: we have to check whether  (p→q)→(q→r) is equivalent to q→r

Q: du ди + 2y ди 2x?y ax az Əx

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Q: b) I = (x-8)² +2=y+3

A: Given that:To find: The value of x.Formula used:

Q: O Determine rand s so that, 3.

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Q: Let u == (7,5,-5) and = (−1, −2, 2). Compute the following: u v . . = 2 7(ū. v) = (7) · v = ū. (77)…

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Q: What’s (E∩F)×(F∪G)

A: We are given that E = {1, 2}, F = {2, 3} and G = {3, 4}.Now, E∩F = {2} and F∪G = {2, 3, 4}.

Q: If x=y+qp and f=xy+qp² Express x in terms of q,p and f

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Q: Evalute ) (2xty)dA, where D=2C2-1にと」 225y41tX)

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Q: 223+-5 -j Suppose z1 = 2+ j, 2 = 3- j2 and z3 = -+j Evaluate %3D 2-a+3-j

A: Substitute the given values of z1,  z2, z3 in the given expression and simplify.…

Q: Find w, x, y, and z so that W X 4 3 8 -3 2 4 -4 |

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Q: Is {(3, 4)}Linear combination of {(1, 2), (2, 4)} show all the work and state why or why not.

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Q: 2. Evaluate: √₁² √2 - x + x da −

A: We know that the modulus function fx=x is defined as x=-x,x<0xx≥0. If we take x=-2, then f-2=2…

Q: X1 Xi + 2x3 , X1, X2, x3 ER – 4.x2 T: R³ → R², T x2 X3 - x3 ||

A: So first we prove that the given transformation is linear

Q: Suppose v4 = 20 – 02 + 503. Let w = 601 + 202 – 303 – 204. (a) Write w as a linear combination of…

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Q: Let floo) = 0e 5 and gloo) = 2a19 Detemine Cgof) (x) 2079. %3D %3D

A: Topic:- function

Q: verify that (AB)T = BTAT

A: Given matrices: Now,

Q: Evaluate: 22 – (8 – j5) z + 40 – j20 = 0 4+j3 O -4+j3 O 4-j3 O -4-j3

A: The roots of the quadratic equation: ax2+bx+c=0 is calculated using the quadratic formula: x1,…

Q: = x° + y*, ¤ = + u, and y = v – u². Find Your answer should be in terms of r, y, u, and v. dv

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Q: e3y dy Vey – 1

A: The given integral is ∫e3yey-1 dy. Substitute t2=ey-1,    2t dt=ey dy in the above integral and…

Q: L{t(u0 – u1) + t²u1}.

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Q: u = ⟨−7, −1⟩, v = ⟨−4, −1⟩, find (a) u ∙ v, (b) u ∙ u, (c) || v ||2 , (d) (u ∙ v)v, and      (e) u ∙…

A: Hey, since there are multiple subparts are posted, we will answer first three subparts.

Q: Let u = (2, 4) and v = (1, 12) and w=(−6, −4). Find: 12. (v.w)-(v.u) 11. 3(u-w)u 13. 2-u 14.…

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