1 -1 2. Let A = and u = 3 -3 -5 -3 (a) Is u in Col(A)? (b) Is u in Nul(A)?

Q: [ 1 If A= -1 0 find x and y such that (xI +yA) = A

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Q: Let [1 2 21 A = 1 1 -1 0 and U = |-2, then determine if 3 -1 2 (i) U is in Nul A. (ii) U is in Col…

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Q: Ex 3.5.1 Let a = 3 .5-7. 13 and b = 2 -* .5.7.11 - 13*. Show that a|b by finding an z such that b =…

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Q: 3 If u = 2– x, J x/2-xdx= 3 - uvūdu A 1 В uJudu .3 O (2-uNūdu (2 – u)/ūdu

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Q: 10 -7 Let u = and v = Compute u • v, v · v, ||u|| and find the dis- 13 16 tance between u and v.

A: Given  u=10-7135 and v=-44316

Q: -1 2 What valuls e a, b, c,d that that mwhe this - 1 - 5 5 consitents - 2 A xc B --- ~

A: We have to check whether given system is consistent or not?

Q: 1. w = sena cos ß 2. W = w u+v 3. f(r,s) = rln(r² + s²)

A: w = senα cosβw is the function of α and βFirst partial derivatives : ∂w∂α = cosα cosβ     {β will be…

Q: 26) If x, y, u, v are variables connected by the relations 1 1 x? =au? +bv2, y² =au² –bv² where a…

A: Given, x2=au12+bv12…1y2=au12-bv12…2 Equation 1+2 gives:…

Q: [â, Ĥ]= [â, tw, thw ato 2. [à, Ĥ]= th w â

A: Zero is the identity element.

Q: α= (5,3,2) y- (-2,3) 2ri-Yj =? i j

A: Summation of each box needs to performed separately. Opening the summation individually and summing…

Q: つ1 BC. T (o,f)= 1 , T(h,f) = (os f. エ、(.T(メ,o)= ズ.

A: According to the given information, it is required to solve the heat equation.

Q: Let  A = (1 1 1, 1 2 2) Find R(A), R(AT), and N(A)

A: Given,A=111122the reduced row echelon form of AMake zeros in column 1 except the entry at row 1,…

Q: - 7 Let v, = 1 6. V3 = -7 and u = 7 Determine if u is in Nul A, where A = V1 V2 V3 6 6 7 6 Is u in…

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Q: 2 =x* x*y, x = s + 2t - u, y = stu; when s = 4, t = 1, u = 2 as' at' du az du

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Q: .3 If U = 2 – x, | x/2- xdx= = n} .3 -J uvūdu В (2 – u)/ūdu | .3 © (2- u)/ūdu 1 (D uvūdu A)

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Q: du = In (– u) + C If u<0, then u (A) True В False

A: The statement is  If u &lt; 0 then ∫duu=ln(-u)+C

Q: If u = (1,0), then Düfz(-3, 4) = ƒxy(−3, 4). True False

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Q: (z + y)? 12. Prove: I = y if and only if ry Note, you will need to prove two 4 "directions" here:…

A: Case1: Prove, x=y if

Q: 13. Given u = and v = , find: a) u + v b) 2u - v c) Ju|

A: Given that u= &lt;-3, 5&gt; and v=&lt;4, -7&gt;   a) u+v = &lt;-3, 5&gt; + &lt;4, -7&gt; = &lt;-3+4,…

Q: 2, z) = 5 and the surfac e at (1,2,3). Evaluate = reasons).

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Q: then Suppose A= G ) and B= ( ) and A is similar to B= M 'AM where M- as O a o, -0 Oba, -1 Oca, -3…

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Q: If z = -4xe³xy and x = √t, y = . Then, the value of dat t = 8 is equal to 3√2 (-1/2² + 2³/1) e + ² 4

A: This question can be solved using the concept of derivatives.

Q: If we have Mactrices : -2 2 :)- -37 2. 3. and 3D -3 Al- Find bo th 2- Create E*F ? 3 - Create FKE?

A: In the question it is asked to do following operations for the two matrices, E=-2023-14131 ;…

Q: If x,+iy, =x,+ iy, then x =y, 1

A: Given there are two complex numbers. They are x1+iy1 and x2+iy2. And it is given that x1+iy1=x2+iy2.…

Q: 2 Let A B = -1 |0 and C = 7 Find x, y,z | 2 -3 such that AB =C.

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Q: 4. Let A %3D {a, b, c}, В %3D {x, у}, and C %3D {0, 1}. Find a) АхВх С b) СхВхА с) СхАх В d) ВxВxВ.

A: Given that: 4. A={a, b, c}, B={x, y}, C={0, 1}   NOTE: As per our answering guidelines, we can only…

Q: If |z-8 <, and ly-히 < , then a - y < 1. 2'

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Q: let R = (-2, 7). Calculate the following: The components of u = PŔ, where P = (1, 2)

A: Given,               R=(-2, 7)   and   P= (1, 2).    The components  of u=PR⇀=?

Q: (-1+i/3)°, by using deMoivre 's theorem

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Q: b) = f ) then prove that x ux + y uy + z uz = 0 u

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Q: Let A = [ L 1 -1 4 24 2 37 2 1 J , V = Is v in Nul(A)? Type "yes" or "no". no Is w in Nul(A)? Type…

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Q: 6. B;? Let B; = [i – 1, 2i + 1]. What is U i=1

A: We will just use the definition of closed intervals of the real number line and the definition of…

Q: (11) Let A = with ei genralues de,2g. Find aeo such that A3 + 12 - 0. (Hint : Cat6)3 = (a3+&3) + 3ab…

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Q: |,x = [] , B = [º,] then,lA| = If A = %3D %3D 1. 16 2. 4 3. S 4. - 12

A: on solving this we get

Q: .3 If U = 2– x, x/2 - xdx= (A) (2 – u)/ūdu В u/ūdu ,1 © Lwūdu uvūdu .3 D J (2- uWūdu

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Q: 2. -4 let u= dx=

A: Indefinite Integration using substitution

Q: 8.Prove the following relationships: a) I(X,Y)=H(X)-HOX/Y)

A: Solution

Q: Let -1 2 2 A = 1 -1 0 and U =|-2, then determine if %3D 3 -1 2 U is in Nul A. U is in Col A (i) (ii)

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Q: 21. xª sen z dz -z' cos z + 3z² sen z + 6z cos z 6 sen z + C %3D

A: see below the answer

Q: If we know P(X = i) = 2/3n2 , i = 1, 2, ..., 6 then E(X) would be?

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Q: et f(x, у, z) %3 ху + z', Р %3D (3, 9, 1

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Q: a- If A = -1 %3D 2 and B = -41 prove that (A + B)T = AT + B". 12 [1/2 - If A-1 =1/2 -1/2) and |A| =…

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Q: make v the subject 1/f=1/u+1/v

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Q: 6. 1 Let W = Span -1 4 and y = 1 What is the distance -4 1 10 from y to W ?

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Q: 1. Let x (x,) E l. Find x if 11-- a. x = 2 %3D

A: This is a question of functional analysis in lp space.

Q: (6) If u, = x-Pa(x)Pn-1(x) dx, show that nu, + (n – 1)u,-1 = 2, | and hence evaluate u.

A: To get the desired result first we will the recurrence formula for pn(x). Then after simplification…

Q: a b be suc b |, then t

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Q: E. Let 2-(e-e(3). Shn that Zy-4(xe ye")=2.

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Q: (b) If y=ae", express t in terms of a and y.

A: