Question 3 Ar = b. ||Ar|| ≤ (a) Show that (b) Calculate (A). In this question, ||- ||- ||-||₁. Let A = -[i], 6=(1,1), 200 ||Ab|| 99 ||b| for any Az and Ab, where A(r + Ar) = b + Ab.

Q: Prove: | a | - | b | <= | a + b |

A:

Q: Let x be a real number. Which of the following is the same as P(Z x) c) P(Z ≤ -x) d. none of the…

A:

Q: Let a . Find al. -

A: Let a→=1, -5, 4. To find a→.

Q: Consider the statement Vxy (y <x) Let x be all natural numbers Let y = x-1 Is the statement true or…

A: We know that the set of natural numbers starts from 1 and it is an infinite set. This set is…

Q: Ex: Let X₂ [1,2,3,4,5]. I. [0,X, [1], 82.3, 81.23], Y. [3,4,5,6,73 andl T₁: [0, X, [4], [4,633 if A:…

A:

Q: Show that if x > 0 and |x² – 9| < 2, then |x - 3| < 1.

A:

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: Pex)=\X+14 aud hex)= x-1 state functions. following domains, of the following 4sing interval…

A:

Q: Is it possible to find a number  n  such that is ∫0∞  xn dxconvergent?

A:

Q: find all real such that 12x-11>x

A: The inequality can be calculated using absolute values. The absolute value function takes a positive…

Q: Evaluate the following commutators [Â, B] = ÂB – BÂ. Hint: use an arbitrary function that cancels at…

A: a x,PxPx=-ih∂∂xx,Pxφ=x,-ih∂∂xφ=-ihx∂φ∂x+ih∂∂xxφ=-ihx∂φ∂x+ih∂φ∂x+ihφ=ihφ∴x,Px=ih

Q: evalnante the folobwing integrationollowing a fferent Path C I'm troid.cpathz pathi Re (3,-2) path3

A: Note:- For part (3) it is not clear that the term written with sint (or coefficient of sint ) is "I"…

Q: Let a 0, and a b? no decision

A:

Q: 2 For 1 X+ 1 and g(x)=, find b. the domain of fo g a. (fo g)(x): a. (fo g)(x)= (Simplify your…

A: Answer: (fog)(x)=2/(x+2)

Q: Let r and s be nonnegative real numbers, f(r) = r" and g(r) = r. %3D Find all pairs r and s such…

A: Given that: f(x)=xr           and             g(x)=xs

Q: 1 f X~ N(0,0²), then X² ~G (¹2¹2) Prove this statement

A: Given  X~N(0, σ2)

Q: Let f : N x N H R be defined by (a + 1)(a + 2b) f (a, b) = (a) Show that the image of f is contained…

A: given that                                           f:N×N→R is defined.…

Q: Let a, be such that asb. Prove that tx Eqt ax cbx

A: Concept: We have a,b∈Q means that a, and b belongs to the rational numbers and a&lt;b means that a…

Q: .Prove that la + b + c| < |a] + |b| + ]c]

A:

Q: |u|> c is true for all real numbers if c _ 0.

A: |u|&gt;c is true for all real numbers if c ____ 0.

Q: Find the value of: 2 100 ;] [*] + x + 100 ] + [~ + + ++ 99 100

A:

Q: Let a = (5,-2, 9). Find ||10||

A:

Q: Show that a|- 16|| < la – b|.

A:

Q: ( n [0,80) = {XER such that x º 403 True or False ? why? TO -10,0)

A:

Q: a+2b 2 Let W = :a,be R}. Show that -4 lies in W. 2a -1

A:

Q: D = 6 -1 3 1 -21

A: To find the trace of a matrix we need to add its eigenvalues or we can add its diagonal elements.