a b If B = find conditions on a, b, c, and d such that c d 1 1 A = 0 1 O b = c Oc = 0 O a = b

Q: Let P(x) = 2x² – 5x – 12 = (1 – 4)(2a +3). Which of the following is true? O A. For 1E[-2/7, 1),…

A:

Q: Let A = {x E Z: 8|x} and let B={xEZ:12]x}. Then A=B АСВ B드 A None of these

A:

Q: Compute | a x b| if a=7 and b| = 5 and a • b=0. (a = 7 ve | b| = 5 ve a • b = 0 ise | a x b'yı…

A:

Q: 27 Find (all) the value(s) of c such that 3c" n= (A) c=3 (В) с— 4 (C) c = - (D) c=} 33 %3D (E) с 3…

A:

Q: a) b) Prove that: ΔΑΒC Δ ΕBD a) E 1 c) ДАВС %3Д СЕА A D E

A: Topic- triangle

Q: s there a formula to calculate:  If A and B are dependent and P (A/B) = 0.35 then  P(B/A) = P (A…

A: A and B are dependent P(A/B)=0.35   we know that, P(A/B)=P(A and B)/ P(B) P(B/A)=P(A and B)/P(A)

Q: The number of the element(s) of order 2 in Z2 O D6 12 1 11 7 15 24 None of them

A:

Q: a + c + e b + d + f 2.) Prove: If r. Then b then (Hint: Let d a = br, c = dr, and e =

A: Given that, ab=cd=ef.  Let ab=r. That is,  ab=cd=ef=r. Then,  a=brc=dre=fr

Q: 3. Show that if fE R(a1) NR(a2) on [a, b), then f E R(cia1 + c2a2) on [a, b] for any constants c and…

A: Given that f∈Rα1∩Rα2 on a,b. Let c1,c2 be two arbitrary constants. Let ε>0 be an arbitrary…

Q: 4. Let v = (2,1), and c = (3,2) such that v.r= 4, and cx = 1. then x = c) (9,14) %3D (5.3) D7-10) d)…

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

Q: a Let A = d f h h i If det (A) = 10, what is the det (B), given B = kd ke kf|? %3D а C -k 10 10k…

A:

Q: 18. Let V, = {* €R | 1 1 1 for each positive integer i. i 4 a. UV; = ? i=1 4 b. nV; = ? i=1 c. Are…

A:

Q: B. Let H « G and K - G, and assume that HNK = {e}. Show that if x E H and y E K, then xy = yx

A: We can prove given result by definition of normal subgroup:

Q: (1) If x + 0, then +0 and A = x. (2) Let a, b e R. a² + b² = 0 if and only if a = 0 and b = 0. %3D…

A: Note: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts…

Q: Let a, b eR with a < b. Assume that a + <b - for all n E N. Show that b- = (a, b). %3D n n=1

A: We will show  two sets are equal.

Q: Given two values x̟ and x, 1. prove that A.M. 2 G.M. 2 H.M.

A: ANSWER: For the give data,

Q: 4. Let c+ d -c a+b . а - с с-d (e+ 2d 20 +1) = (d c a). %3D for some a, b, c, d ER. Then a + b+c+d%D…

A: To find  The value of a+b+c+d

Q: Let X = P(A) and E(3x) = E(2-6x) find A.

A: Solution: 46. From the given information, X follows Poisson distribution with parameter λ.

Q: Let A = {x E R : 2 < x < 3} and B = {r €R: -1<r< 2}. Prove that |A| = |B|.

A: To prove this result we first show a objective map from [-1,2] to [2,3]. Then (2,3) is uncountable…

Q: 9 D Let A = d e f g hi b e f h i a a e Find k such that |A = tr A = 0 = A1234 = ck A².

A: Given: The matrix A=abcdefghi and the quantity z=abde+acgi+efhi   To find: The value of k such that…

Q: b. If A = 3 x and A = AT, then: x=0, y=0 None of them. O x=y O x+y=0

A:

Q: · (b + c) = ² 7. Prove that à. = a · b + ac for all a, b, c € R³.

A:

Q: Let X P(A) and E(3x)= E(2– 6x) find a.

A:

Q: Q1) If B = B-1 then B = I or B = -I. Prove or give counter example. %3D

A: A detailed solution is given below.

Q: Show that e = (1 + i)/√2 if and only if z = (n/4+2km)i, k = 0.±1, +2...

A: This question is related to complex numbers,  we will solve it using given information.

Q: 3. Determine whether each of these statements is true or false. а) ОєФ b) Ø E {0} c) {0} c Ø d) ø c…

A: We know that ϕ is subset of every set. And a∈A if a is an element of A.

Q: TRUE/FALSE If A = A−1, then A must be equal to either I or −I.

A:

Q: R.1. Suppose A – BC Cn D and x E A. Prove that if x ¢ D then x E B.

A:

Q: If P(A) = 0.45, P(B) = 0.40, %3D %3D and if A and B are independent, then P(AUB) equals a. 0.63 O b.…

A:

Q: Ex let x be with pmf 1=,2,3, 16 O find c P(X)2)

A: We want to find the value of c and P(X≥2) and P(X2=9)= ?

Q: 27. Let a, b eR 3 a> 0 and b > 0, A = (0, a) and B = (0,b). If D = {xy : x € A and y e B} %3D then…

A: Option (C) is correct.

Q: Use C.P. and/or I.P. to prove the following.  a) 1. (A ∙ O) ⊃B 2. B ⊃~O 3. A ⊃O…

A: Note: The symbols and format in Part c are not proper, so we will solve the sub-parts a and b.…

Q: 7. Let w = 8x? + 6 y² +2z° ;x = r²; y =t*; z =r² Find A) -321 + 481- + 201º В) -321 +481' + 201° - =…

A:

Q: If P(A) = 0.40, P(B) = 0.35, and if A and B are independent, then P(AUB) %3D %3D equals a. 0.89 O b.…

A: Given - P(A)=0.40  , P(B)=0.35  We have to find P(AUB) if A and B are independent. P(AUB) is defined…

Q: Let A = {x e Z: 10|x} and let B={xeZ:15|x}. %3D Then * O Bc A O A=B O None of these O ACB

A: Suppose A and B are two sets . Note the following result : If x∈B for all x∈A then A⊆B . If A⊆B and…

Q: 20. Let D = {r € R: r > 0 and a² a E. None of the above.

A: Upper Bound :  Let A⊂ℝ and suppose M∈ℝ .If  M≥a for all a∈A then M is one of the upper bound of set…

Q: Let z x²y – xy², x = e-24, y = e2t, then which of the following is a. 2et + 2e 2t O b. –2e2t – 2e-2t…

A:

Q: а b ст Let A = d e fand B [d+2g e+2h f+2i] b |If det(A)=-1, then det(B)- а %3D g _h -3g -3h -3i

A:

Q: Let W= Span{2+², 6+t²}, then dim W= Select one: a. None of these b. 2 С. 1 d. o

A: As a first step we need to find out if the vectors in W are linearly independent. Hence, consider…

Q: · (b + c) = a · = a · b + a · e for all a, b, c € R³. . 7. Prove that a.

A:

Q: Compute the indicated quantity. P(A) = 0.7, P(B) = 0.2. A and B are independent. Find P(An B). P(A n…

A:

Q: Let X1,., X idN(µ, o²). 3(x2 + + Xn-1), Xn X1 If u = ... 5(п - 3) 5 | find E(@) 3 (a) 5 (п-3) 3…

A:

Q: Compute the indicated quantity. P(A) = 0.3, P(B) = 0.3. A and B are independent. Find P(A N B). P(AN…

A: Property : if A and B are two independent events with probability P(A) ,P(B) then P(A∩B) = P(A) .…

Q: Let C: |z-i=3 and I = §. e2z -dz. Then 22 I= 4ni O I= 8ni |= 6ni |=0 O None of these

A: .

Q: Let z = a?y – ry?, x = e 4, y = e2t, then which of the following is 2e2t + 2e 2t a. O b. -2e2t – 2e…

A:

Q: Let X-bin(6,0.57), then P(X=2) is equal to: O a. None of these O b. 0.293 O c. 0.325 O d. 0.167 O e.…

A: Binomial Distribution: If we have n trials each having two outcomes, say Success and Failure, trials…

Q: Let a, b e R with a < b. Assume that a + <b - for all n E N. Show that 1 = (a, b). a + ,b n n=1

A:

Q: (5) If A e Mn(R) with A³ = 0, show that (I+A) is nonsingular with (I+A)-' = I – A+A (6) If A, B e…

A:

Q: 1. Find all numbers z such that Az' + Bz2 + Cz = D [2 4 2 A = 2 4 2 1 B = 3 1 - 2 3

A: Given A = 242131B = -1111-2-1C = 242131D = 1-1-1-121 Clearly C=AD=-B

Q: If P(A) = 1 P(B) = 2 and P(A U B) 11 find (i) P(A/B), (ii) P(exactly one of A and B occurs), 12 4…

A: