Find A V Al2) v Al3] , given [1 0 01 A = |1 0 1 lo 1 ol

Q: Prove that ||A||1 = maxi<j<n{E#1 laij|}. i=1

A:

Q: QR MN ZN = ZR QS MP RS Given: NP Prove: R N

A: In △MNP and △QRS QRMN=RSNP=QSMP

Q: 00 fcos(x*) dx = ! Ex. 41. Prove that 2 V2 0.

A:

Q: 12. Given: RX ITTW Prove RS ST = WS SX I

A: Find the solution below

Q: Prove that Vn > 0: 2º + 21 + .…+ 2" = 2n+1 – 1. ... an+1_1 Prove that Vn > 0: aº + a² + .….+ a" =…

A: Here, the objective is to prove the following: 1) 20+21+22+......+2n=2n+1-1   ; n≥02)…

Q: Let x, y, z e Z Prove that if x – 2y + 3z is odd, then 4xy – 6z is even.

A:

Q: Let x, y e Z. Prove that if 3x+7y is odd or 5x + 6y is even, then x or y is even.

A: We have given that for x,y belongs to integers. If 3x+7y is odd or 5x+6y is even then x or y is even…

Q: Let x, y, z E R. Prove that if x – 2y + 3z is odd, then 4xy – 6z is even.

A:

Q: dr Evaluate J z(z²+1) Select one: a. In(- 2+1 b. In2(- c. In(1 2z с. 7²+1 d. įin(

A: To evaluate: dxxx2+1

Q: Prove that the following relationship is true: nCr + nCr + 1 = n + 1Cr + 1

A:

Q: 6. Given: ZP=ZR; ZQ= ZS Prove: PO| RS P. 'R

A: ∠P≅∠R,∠Q≅∠S

Q: If u = x3 -3xy and v= 3x2y-y3, prove that Pu/Əx2 + Pu/əy2 = Pv/ax2 + Pv/@y²

A:

Q: Show and use d(Xn, FCN))<« d(Xn-1 'x) Vny? To prove X = fx) %3D

A:

Q: 7. Let Te L(V, V). Prove that T2 = 0 if and only if T(V) c n(T). %3!

A: See the attachment

Q: J prove that for 0 <r<R

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Q: Prove that i 224 s 2xP for xzO, y zo i and 1 t L-l with p>

A: Given that x,y≥0. And 1p+1q=1 with p&gt;1. Consider gx=xpp+1q-x. Then g'x=xp-1-1 and g'x&lt;0 when…

Q: 3. Let A = {8k +7 : ke Z} and B = {4j+3 : j e Z}. Show that AC B. %3D

A: I am solving only Q3,as you mentioned.

Q: o prove that knVA=| Test the seuence (ConViordív) of (10) an = (^_-) ) an 15 ら 9n: 3ntl 3n-1 (の+ (7)…

A:

Q: Let P = {p:p=6x-1, for some x EZ} and Q= {q:6y+5, for some y EZ). Prove that P= Q

A:

Q: Let x e R,-1. Prove that VNEN (1+x)" >1+ nx

A:

Q: Prove that for Vr > 0, s > 0, √√r + √√5 ± √√r + s r, s

A: # As per the guidelines we are entitled to solve one question at a time please resubmit the other…

Q: Prove that (aA + bB)t = aAt + bB t  for any A, B belongs to Mm× n(F) and any a, b belongs to F.

A:

Q: 4. a) Prove that i) V=I ii) fx+nh = ! I+A 1+A (1) AK fx. = 4k=0

A: Introduction: In numerical analysis, there are many different operators that are used. These…

Q: Show that the following cosh 3 (0,0) r(3,5) x² y?. (10xdx +6ydy)

A:

Q: Let a,b E R with a # 0, b # 0. Prove that (ab)¯1 = a°1b´1. %3D

A:

Q: 28. (a) Prove that for x e R" and s < t, Ds(x) C D;(x).

A: The notation Dsx represent  an open ball of radius s, centered at x∈ℝn. Let x=x1, x2, …, xn,…

Q: (a) Let r = ri+ yj + zk and let r = ||r||. Prove that - (1) a

A:

Q: o.10. Prove that (a) J,"(x) = ¿[J,(x) – 2J,(x) + J, + glw). n n-2 n' n+2

A:

Q: a) Let Z = 7 – 13i, find: i) Im ) ii) (Re Z)?

A: Complex Numbers: The complex number is basically the combination of a real number and an imaginary…

Q: 6. Use Green's Theorem to evaluate O (y* – xy?) dæ + (2 – a*) dy where C is shown below. y -2 ² +y²…

A: Green's theorem

Q: 7. a) Prove that for r > 0 * (E) + c. Vr2 – r²dx = vr² – x² + -1 sin 2 +C.

A: To prove: ∫r2-x2dx=x2r2-x2+r22sin-1xr+C

Q: A := {x € (0,1)|x= ar, for some r € Q} re that sup(A) = 1.

A:

Q: Proue that || A|1maπi <j <n 1 Σajl . m

A: In the given question we have to prove that   A1 = max1≤j≤n{∑i=1maij}                         (1)the…

Q: Q(x) = √3/2+² Ser fet de Prove that & QQ (-∞ ) = 1

A: Here we can use Gamma function formula Γn = ∫0∞ xn-1 e-x dx to evaluate the given improper integral.…

Q: Prove that x" dx „n+1 + C, n + 1 for n + -1.

A:

Q: 1. Prove with the usual notations that: (b) A + V =- (a) EV = VE = A (c) A= SEZ

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 19. Given: PR || VO; RO || PV; PR = RO Prove: 1 and 22 are complementary. R V. E.

A:

Q: FIND THE UNTQUE SOLUTION OF AU= 0 34/x1<4 SUCH THAT U(x) 5 on x =3, U(x)=6 on /×/ =4 on 2 in R in R…

A:

Q: dv Prove that 4u/2n

A: We use Gamma function to prove the given result.

Q: 9. Let S- {xeZ| 3r.seZ,x=9r+6s) and T={xeZ| 3x} b) Prove that T Cs. a) Prove that SCT. Hint for (b):…

A: Part(a) We have S=x∈Z/ ∃r,s∈ℤ, x=9r+6s and T=x∈ℤ 3/x  Now, let a=9r+6s be an element in S. Then…

Q: Given: S 5x² cos 3x³dx. If u = 3x³, then the resulting integral is S f(u)du. Find f (*):- ... 5/7…

A:

Q: 10. Given: YT = YP, LC = LR, Proof ZT= LP Prove: CT = RP R

A: Consider

Q: 03) find the ax en the sl abetwed wol y=J2-X, and y= 0

A:

Q: Find a mat rixP such that P [1 2 1 0 | 1 0 P = O A. -1 1 1 - ОВ. 1 P= OC. 0 1 -1 0 P = O D. 1 1 1 0…

A: Just multiply both sides by P from left side and set P as 2×2 matrix.

Q: 7. Find T, N, ar, an at t=n. r(1) = 4cos(1)i–4sin(r)j-3rk

A: Tt = r'(t)r'(t) and N(t) = T'(t)T'(t) aT = r'(t) .r''(t)r'(t) and aN = r'(t)×r''(t)r'(t)

Q: B. Prove by direct proof general. P: Vn e ZE, (n – 1) (n+ 1) e Z,

A: I have solved B; you just need to expand (n-1)(n+1) and then use the fact that square is always…

Q: Let x, y,p E Z, where p is prime. Prove that x2 – p²y – p + 0. (Hint: you may use without proof that…

A: Solution :-

Q: Let x, y e Z. Prove that if 3x + 7y is odd or 5x + 6y is even, then x or y is even.

A:

Q: Let P= (p:p=6x-1, for some x EZ) and Q = {q:q=6y+5, for some y EZ}. Prove that P=Q

A: