7. а) Prove that (ӑ — Б) х (ӑ+Б) %3 2ӑ х ѣ.

Q: 1. Let A = {a, h, g}, and B = {3,6}. Answer each of the following questions. %3D (а) Ах В (b) В х В

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Q: 2. Let L1 bg 3D (-1,2, 1,3, 3), сі %3D (3, —4, 0, — 4, 3), сэ %3D Find a basis of Lin L2 and L1+ L2.…

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Q: Assume A = 21 2] and B = 1 3 [43] [4 3 11 7 6 show that (AB)' = B' A'

A: Given matrices A and B, To show that AB'=B'A'

Q: الوقت المتبقي:1 ساعة، 04 دقائق. 07 ثانية )ثوان(۔ حالة إكمال الأسئلة: 18 Jlgull find the product AB…

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Q: a=(3,2,-1), b=(1,-1,2),

A: Given: a=3, 2, -1 and b=1, -1, 2 To find:  1. a×b 2. a+2b×b 3. a·3b 4. b×a·c 5. b×3a-2b

Q: 4- Suppose that A = {x1 = (2,0,1), x2 = (1,–1,4), x3 = (-1,–2,1)} and B = {y, = (-1,0,2), y2 %3D %3D…

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Q: (7- 8)2 | /8-ん (e-)」ade-)|I/8-ん Hence, 2By < 1, (7 – 6)2 vhich can be written as |a(y – 8) + 3||y –…

A: I have only deducted the green part as per your request.

Q: [4 -1 1 2 B = 3 5 1 2 3 For items 1-2: Given A = ,D=-2,E=[1 -1 2]. Find -1 0 -2 1 1. A? – 3B – 13 A.…

A: A system of m×n numbers arranged in the form of a rectangular array having m rows and n columns is…

Q: (1 3 A = 2 1 4 0 3 B = -1 -5 6. Evaluate A+B , 3A– 2B , AB', A'B .

A: If the rows and columns of the matrix A are interchanged, then we obtained the transpose matrix, AT.…

Q: b) Use the initial condition x(0) = 2 to find the particular solution of dx - 2x = 2e3t dt

A: We have to solve the given initial value problem  As per the answering guidelines we need to answer…

Q: (b) Show that (АВ) -1 — в-1А-1. (АB) -1 B-A-1

A: In this question we have to prove AB-1=B-1A-1. we know,X-1=1Xadj.A

Q: 9. Assume that the stated inverses exist, prove (A+ B)-1 = A-'(A-1+B-!)-'B-1.

A: Here we prove a equivalent statement.

Q: 9. If an+1 = 2an + 2 and ao = 4, then an = O 3(2)n + 1 6(2)n-2 O 2n + 3 O none of these

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Q: Question 1 Is it possible for one of (oA) A 0 and o A ( e) to be true and the other false? No, they…

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

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Q: 3.) -бп — 20 %--2n + 4(1 — Зп)

A: solve the following

Q: a communication source emitting the following symbols S = {a, a2,a3}. Find P(a,) if 1. P(a,) = and…

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Q: 2 2 1+ 5+² µ² = (1 + 2/² ) E" - M+² = 2

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Q: (a) If a, b,c € Z+ and a +b=c then (c,[a, b)) = (a, b).

A: As you asked multiple questions , so I solved only the first one.

Q: For n 2 3, the series 2+4+6+..+ 4(n) can be equivalent to .. ...... OA. n? +3 B. n +1 C. 3n2 + 4 OD.…

A: 3.  2+4+6+...+4n is equivalent to the option (A).

Q: Let 7(u,v)-(u, v, u+v), then the second fundamental coefficients are: 2 1+4u+4v² ,M= V1+4u+4v a O 2…

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Q: 13. If A = Find A + A! -5 B. D. -5] 5. 50 A.

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Q: 6 -1 Let A =| 0 -2 and B . Compute (AB)". Show your work. 4 3

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Q: If V = (x² + y² + z)² then - If V (x² + y² + z) % %3D 1) 0 2) 1 3) x² + y? + z² 4) 2

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Q: 1 for x. 2 Solve - x+1 -+ 5 =

A: The given equation is                                               2x+1+5=1x

Q: 1 If x is a real number, then is x² + x4 equal to а. V1 + x² b. 1 xV1+ x? c. xV1+x² d. æ|/1+ x² 1 е.…

A: Let's find.

Q: If 1 A = -9 6 1 6. 2 -T and Q(#) = ' Až, then Q(z1, 12, T3) = Enter z1 as x1, 12 as x2, and 13 as…

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Q: 28. Evaluate : a) A (3e) b) Aʼ(ab)

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Q: 2-3 [84] 5 -2 - [ ² - 3] · B = [$ 3]), and C = [; } 2. Verify that -4 6 55 3 - Let A = AB = AC and…

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Q: 3 4 10 find -2 -5) 5 If A = 8 and B = 1 1) (а) (АВ)" (b) В'АТ

A: Solution

Q: prove that

A: Given: prove that 1aa21bb21cc2=b-ac-ac-b For proving given determinant, we apply operation R1→R1-R2,…