5. Let (1 2 3 A = 2 1 4 1 0 2 Find A-lif possible. If A-does not exist, explain why.

Q: 1: Prove that (c a) * H = (c b) * H implies that a H = b H

A: Given an equation. We need to prove that : a*H = b*H where H is a subgroup of a group ( say G). Also…

Q: (-1)"2" /ñ Prove that if m is a positive interger, 1'(-ni +3) =1:3.5...(2m – 1)

A: I will use method of induction to prove the statment.

Q: 1. Show that for all z1, Z2 E C, Then we have: |Z1 + Z2| < |Z1| + |Z2|

A: Using complex properties.

Q: prove if P>-l then Citp = I+np %3D n€ IN

A: The given statement is not TRUE. Counter example is taking n = 2.

Q: Show that 1/2 ( Tn + Mn ) = T 2n

A:

Q: 1 Show that 2-* d.x 2 In 2

A: We can show the answer in the following steps.

Q: -3 2. Evaluate: V12-피 + z dar 0,

A:

Q: Prove that if a eZ then the only positive divisor of both a and a+1 is 1.

A:

Q: 26 a ba Q(1E) = }a+bV2 / a, be Q4 2.1) Show (K,t,') eld under add. and rmult, of amotmias 2.2) Show…

A:

Q: 2.If alb and alc then al Cbx tcy) for all X>YEZ.

A:

Q: b) If d = 1, prove that (1 if a is odd gcd(a, 2b) %3D if a is even

A:

Q: Show that when |z +1| < 1,z² =1+£(n +1)(z+1)" n=1

A:

Q: 2. Prove that if 5BA+ AC A - I = A, then A must be inver

A:

Q: 2, 5x .3 b) Y = In 60(х, + + X, 2. 3.

A:

Q: 5. Prove that if A and B are similar then dim(ker(A)) = dim(ker(B)).

A: We have to prove dim(ker(A)) = dim(ker(B)).

Q: 2. Prove that if AB = AC, then B need not equal C unless A is invertible.

A:

Q: 2 2 22 if== prove that 22 a¯x +b¯y¯ +c¯=¯ 3, ,3, 3 a'x + b°y +c°z xyz abc %3D

A:

Q: Show that for all z1, Z2 E C, Then we have: |Iz1| – |z2|| < |z1 +z2l

A: 2) The inequality can be proved as follows:

Q: PROVE that 2a + b = 0.

A:

Q: verify that (AT )T = A

A:

Q: (16) Show that AB=BA for 0 0 0 3 0 0 0 1 A = and B = 0 3 1 2

A: A=-100030001 and B=500030002

Q: 13 3. Use the IVT to prove that y = r Inr has at least one zero on 2 2

A: Above function is continuous function in given interval. So we can apply IVT

Q: 1. Show that for all z1, Z2 E C, Then we have: |Z1+ Z2| < ]Z1] + |z2|

A:

Q: Is z(√2) isomorphic to z(√3)?

A:

Q: @ Let A -a Find Cenditiens on a,b.c and d that AX =o has infailely many Solution. what must there…

A:

Q: 3. Prove that Re(2-+z')<4 when z<1.

A: a.          x+y ≤x + y                                             (triangle inequality)b. Re(z1+z2)…

Q: Prove that if a, b E Z - {0}, then gcd(a, b) = gcd(a, -b)

A: soln:gcda,b=Greatest common divisor of a and bEvery integer that divides a and bsimultaneously will…

Q: (1) Use the definition to prove that if xn → 2 then (2xn + 1) / xn → 5/2.

A: As per our company guideline we are supposed to answer only first three  qs, kindly post remaining…

Q: Prove indirectly: "V n E Z, 4 ł (n² – 2)."|

A: Ans:Let us assume that 4/n2-2;∀n∈zthen we have there exist a positive integer k such…

Q: (2 Let xinN(0.1), n = 2 and T= Xx +X2 Show that Tis a Sufficiency Stakistic.

A:

Q: It is possible to regress x1 on y. a. True b. Falas

A: From the given dataset we have to check that , is it possible to regress X1 on Y1  or not.

Q: 15. prove that L. d= nd(n)/2

A:

Q: 21. Find af and of if f(x,4)= 3x" +2xy+ Sy , x= 4v? + Bn", and u 2v-w? Vour %3D 4= 2v-w? Vour av…

A: We have to check

Q: Let A find on Conditions a,bic and d has infinitely that AX =o many solution . what must there Pere…

A:

Q: 4. Assuming that gcd(a, b) = 1, prove the following: (a) gcd(a +b, a – b) = 1 or 2. %3D %3D

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: Suppose A · B = 0. Show that this implies that C(B) is contained in Null(A).

A: Suppose A.B = 0 then we have to show that  Column space of B contained in the null space of A  i.e…

Q: prove that and = nd(n)/2

A:

Q: es lls ew zeiflucifiib ons einiseen stigesber Show that for neN, (2n)! ' (r!)² ((n −r)!)² - 7=0 2n -…

A: We will use binomial expansion to prove given relation

Q: 6. Prove that, if a, b e Z, then 3a? – 4b – 5 0. - -

A: Answer

Q: 3. Let, a1 = 3,az = 4 and for n > 3, an = 2an-1+ an-2 – 5, express a, in terms of n. %3D %3D

A: An arithmetic progression is a sequence of numbers such that the difference d between each…

Q: how that ℝ3 = span( 1 1 2 1 2 1 0 3 -1

A: We want to show that  any vector can be written as linear combination of the three  given vectors…

Q: 2. Suppose that {v1,... , Vp} is an orthonormal set in R", and that x E R". What can you say about…

A:

Q: Prove that where e, > (1,0)"

A: Prove that     conve1, e2, -e1, -e2=x∈ℝ2 : x1+x2≤1 where e1=1, 0T , e2=0, 1T.

Q: True or False? If d = gcd(a,b), then there exists integers x, y such that d = ax +by

A: solution.

Q: (a) Show that for x > 0, 1 5a' < In(1+ x) < |

A: As per guidelines, we will solve only first part. Kindly repost other part separately.

Q: Let 0 3 0 6 3 A = B = 1 0 1 O 2 0] 3 -2 -4 C = 3 -2 -4 3 6. 3 7 (a) Compute AB. AB = (b) Compute AC.…

A:

Q: #02:-Discuss all the cases of reducible to hamggenou D.E form.

A:

Q: 12. Prove the following (A+ BB")-B= AB(I+ BT AB)-1 by express the B+BB' AB in two forms. O Type here…

A:

Q: 4. Show that: do Tb/(a? – b²) - a+bcos0 а b2 Where a>b>0 such that * -1+ 1. < 1 - a²

A: To Show: ∫0πdθa+bcosθ=πba2-b2 Concept: i. 1+tan2x=sec2xii. cos x=1-tan2x21+tan2x2iii.…

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.