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

Q: 11 6 linear combinations of x, y, and z, or show that it cannot be done. Let x = 120 and z = TTTT If…

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Q: 2. Let A = 201-18 and /= 2 1 1 2 01 Find A(A+1).

A: A=[2 1      1 2]I=[1 0      0 1]

Q: Let a=⟨3,−5,5⟩ and b=⟨−1,5,2⟩ Find the component of b onto a

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Q: A. Let u = (1, 2, 3, 4), v = (0,2, t, 3), and w = (1,1,1.1). „Find t so that the angle between u –…

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Q: Let X={a,b,c,d), f = ((a,b),(b,a),(c,c),(d,d)}CX×X, and g= ((a,d),(b,a),(c,b),(d,c)}CX×X. Find gof.…

A: Use the definition of composition of functions to solve this problem as in next step.

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

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Q: 3. Which of the following statements are true? There may be more than one correct answer. A. Ø CA B.…

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Q: Show that if AB = I, then det(A) 0 and det(B) # 0.

A: Here given as AB=In find determinant both sides detAB=detIndetAB=1

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: Show that A × B ≠ B × A, when A and B are nonempty, unless A = B

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Q: Exercise 2. Prove that if A = B and C z D, then A × C = B x D.

A: Given data: A≈B......(1)C≈D......(2) The objective is to prove A×C=B×D

Q: Let A = {a, b, c, d}. Find P(A).

A: Let A = {a, b, c, d}. Find P(A).

Q: Compute u – 3v, u v and u x w.

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Q: Suppose gcd(ab,c)=1. Prove that abc | d if, and only if ab | d and c | d.

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

A: Given, A={2,y,z} B={3,x,z} How many distinct elements are in (A×B)∩(B×A) ?

Q: true. Show that (a v bc)(a Abc); but the converse is not

A: Solution:

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: The linear combination of gcd(252, 198) = 18 is? a. 252*4 – 198*5 b. 252*5 – 198*2 c.  252*5 – 198*4…

A: Given, gcd252,198=18 We, can write the above equation as, 252=1·198+54198=3·54+3654=1·36+1836=2·18+0

Q: Let A = {a, b, c}, B = {x, y}, and C = {0, 1}. Find A × B × C C × B × A C ×…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: If A={1,2}, then A x A =

A: Given data, A = [1,2]A×A =(X1 ,Y1)×(X2 ,Y2)= {1,2}×{1,2} A×A =(X1 , X2) (X1 ,Y2) (Y1 , X2) (Y1 ,Y2)=…

Q: . Let A Find A.

A: Given matrix is Firstly, we find A^2

Q: Show if gcd(a, b) = 1 and a\x and b\x Then a b\x

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Q: Consider the vector field F(r. y, 2) = (6yz- 8z) i + (10y + Gu z) j + (6æy – 9c?) k. a) Find a…

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