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

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

A:

Q: Prove that Master Cheng has won precisely 21 times in a row during some consecutive days.

A: Please find the solution

Q: 3- Suppose u, v EV and||u|| = ||v|| = 1 and = 1. Prove that u = v

A: Given: Vectors  such that ,  and .To prove that .Concepts used:Inner product space:Let be a vector…

Q: Let S=X belongs to R: x> =1. a) Show that the set S has lower bound, but no upper bounds. b) Show…

A: The answer is given as follows:

Q: Prove: If a &gt; 0, then (1/a) &gt; 0.

A: It is given that a&gt; 0.It is known that if ab &gt; 0 then a &gt; 0 or b &gt; 0 or a&lt; 0 or b…

Q: Use proof by contradiction to prove that if x + y &gt; 2, then x &gt; 1or y &gt; 1 (or both).

A: The method of contradiction is used to prove a statement or a set of statements. The inverse of the…

Q: Let x € Z. Prove that if 3x + 7 is even then x is odd.

A: , then we have to show  is even then  is odd

Q: Prove that if A and B En and Ac B, then

A:

Q: 14. Statement Reason 1 ZA D 1. given D. Prove: BX • CD = XC • AB

A:

Q: 2. (6 marks) Let a, b, c € Z with a 0. Prove that if a X (a + 2b + 3c), then a Xb or a Xc.

A:

Q: Let α belong to Sn. Prove that |α| divides n!

A: The symmetric group ​ is the group of permutations on n objects. Its order is .

Q: Let S= {n | n=5 k+ 4 for some integer k} Let T= {n|n=5 j– 1 for some integer j}

A:

Q: Prove that ||A||1 = max1<j<n{£", |aij|}. %3D

A:

Q: GIVEN: k || l, 5 = x8. PROVE: j || l. 56 3 4 1 2

A:

Q: Prove than any pair of elements in H can be mapped to the positive y-axis by an element of SL(2, R).

A: According to the given information, it is required to prove that any pair of elements in H can be…

Q: et x + y+ z=5 where x, y, z E R. Prove that x² + y² + z² >

A:

Q: Find c such that each of the following is true. a) p(0 c) = 0.8212

A: We have to find given z score.

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

A:

Q: Let n E N coprime with p. Show that there exists x, y E Z coprime and such that p | x² + ny² is and…

A: To prove the given claim we have to show that :- x,y ∈ Z ; gcd(x,y)=1 ; p | x2 + ny2   implies…

Q: Prove: Provided it exists, (A-1)¯ = A.

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Suppose u, v belong to V. Prove that = 0 if and only if ||u|| ≤ ||u+av|| for all a belong to F

A: We have to prove  if and only if

Q: . Consider the statement: Let A, B ∈ Z. If 6|A and 10|B, then 4|(A2 + B2). (a) Prove the statement.…

A: 5. Consider the statement: Let A, B ∈ Z. If 6|A and 10|B, then 4|(A^2 + B^2). (a) Prove the…

Q: Prove or disprove: If (xn) and (yn) are subsequences of each other, then xn = yn.

A: Definition: Suppose ann∈ℕ be a sequence. A subsequence of this sequence is a sequence of the form…

Q: Suppose x, n ∈ N and n not equal to  0. Then, show that xn is positive if and only if x is positive

A: Given that x, n∈N and n≠0. According to question, N=0,1,2,3,4,5........ First suppose xn is positive…

Q: Prove: For c &gt;= 0 , | a | &lt;= c if and only if -c &lt;= a &lt;= c

A: