Prove that if A – B – D and B – C – D, then A -C– D.

Q: Let u = (9,3,-3), v = (0,2,-5), and w = (6,5,4). Compute v X w. vxW=(

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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: Let A= {1,2,x,y,z}, and B= {1,2,3,z}. How many distinct elements are in (A*B) intersect (B*A

A: Given that A=1,2,x,y,zB=1,2,3,z To find the number of distinct elements in A×B∩B×A:

Q: True or False? a1 a2 independent. If True b₁ # 0, then the subset {(a₁, a2), (b₁,b₂)} of R² is…

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Q: The rank and the nullity of A, respectively are 1 2 3 11 0 0 1 5 0 0 1 2 000 0 A = a. 1,3 b. 2,2 c.…

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Q: me Ik Pi p then

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Q: The rank and the nullity of A, respectively are 1 2 1 2 1 0 0 1 2 1 A= 000 1 2 0 0 2 4 2 0 00 4 8

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Q: Prove that if CE AB and C+ A, then AB AĆ.

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Q: 6 -1 -2 -3 0 2 0 1-2 nations of the columns of A. . W is the • Is b € W? . In one line (with minimal…

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Q: Ema thinks that (u) xw, exists. Paul disagrees with her. Who is right? Explain why.

A: Dot product gives a scalar value  .

Q: E. Show that both R and R² may be covered by countably many open balls.

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Q: Let S = (a, b, c, d, e, f with P(b) = 0.16, P(c) = 0.12, P(d) = 0.29, P(e) = 0.22, and P(f) = 0.11.…

A: Given S = { a, b, c, d , e , f } P( b ) = 0.16P( c ) = 0.12 P( d ) = 0.29 P( e ) = 0.22 P( f ) =…

Q: Exercise 3. Suppose that A and B are independent. Argue that A' and B' are also independent.

A: P(A⋂B)=P(A)P(B)  when A  and B are independent.

Q: Prove that if A CC,BCC, and (C \ A) C B , then C = AU B.

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Q: Exercise 1. Let n be the year of your birth. Compute the following [ 10] 2 -2 2 1 using…

A: Theorem A matrix is diagonalization if and only if it has n distinct eigenvaluesAnd A can be written…

Q: (b) Let A and Bị be independent; similarly, let A and B2 be independent. Show that in this case, A…

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Q: 1. Determine whether b is in the column space of A, and if so, express b as a linear combination of…

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Q: If then A-¹- = A = [1 0 0 07 3 1 0 0 24 1 0 8 55 1

A: The given matrix, A=1000310024108551 We have to find an inverse matrix of A.

Q: 10 Jlgull et S={1,3,5,. . .;2,4,6, .}, then s(7) = {1,3}.a O {1,3,5,.. .}.b O {1,3,5}.c O…

A: Given a statement

Q: 3. Determine if b is a linear combination of a₁, a2, and a3. 2 3 a1 = 1 , A2 = 2 , az = 1 b= 4 1 1 0…

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Q: 2. List all elements of A = M₂ (Z₂). Give the units in A, as well as the zero divisors in A.

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Q: Suppose a, b, c, d e Z, a + b = c, and dla. Prove that d|b if and only if d|c. 5.

A: see below the calculation steps

Q: Compute u – 3v, u v and u x w.

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Q: 4. Let A

A: Given,                A=1, 2, a, b, ϕ

Q: Show that both R and R² may be covered by countably many open balls.

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Q: Write the set containing two females in terms of A and B.   e. List the elements in !A, AB, AuB…

A: According to the given information, S=JD, JM, JS, JN, DM, DS, DN , MS, MN, SN A=JM, JS, JN, DM, DS,…

Q: Let a, b, c E Z. show that ca & cb if and only if c (a, b).

A: Division properties are used to prove it

Q: Find u - v, 2(u + 3v), and 2v – u. u = (5, 0, -3, 8), v = (0, 2, 8, 5) (a) u - v = (b) 2(u + 3v) =…

A: The objective of the question is evaluate the given values.

Q: Let A; = [i, i + 1], i = 1,2, 3, 4,... Then A n A2 N A3n A4 is O A. {1} O B. { } O C. [1,5] O D.…

A: We have Ai = i, i+1 and i = 1, 2, 3, 4 (we need to consider only up to 4 since we have up to A4…

Q: Let S = {a, b, c, d, e, f} with P(b) = 0.21, P(c) = 0.25, P(d) = 0.2, P(e) = 0.1, and P(f) = 0.11.…

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Q: Suppose a, = lan 1- 6an 2 + lan 3 and a4 = 47, as = 3, and a6 = -273. Find a1, a2, and az. %3D %3D =…

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Q: Prove or disprove that if (A U B) C (An B), then A = B

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Q: Let e; = [0, ...,0, 1,0, . .., 0], where 1 is the ith entry. Show (a) e;A = A¡, ith row of A. (c) If…

A: Solution: Let ei=0,...,0,1,0,...,0, where 1 is the ith entry.

Q: Suppose that P ( A ) = 0.4,  P ( B ) = 0.5 and A , B are disjoint. Compute P ( A c ∪ B c ) .

A: From the provided information, P (A) = 0.4, P (B) = 0.5 The events A and B are disjoint.

Q: Let S = {a, b, c, d, e, f} with P(b) = 0.13, P(c) = 0.19, P(d) = 0.3, P(e) = 0.12, and P(f) = 0.15.…

A: P(a) = 1 - {P(b)+P(c)+P(d)+P(e)+P(f)} = 1 - (0.13+0.19+0.3+0.12+0.15) = 1 - 0.89 = 0.11 So, P(a) =…