3. Prove that (An B)² C A × B.

Q: 1: Prove that (c a) * H = (c b) * H implies that a H = b H

A: Given an equation. We need to prove that : a*H = b*H where H is a subgroup of a group ( say G). Also…

Q: Prove that: 1- Ā. (B × C) = B . (Č × Ā) = C . (Ā × B)

A: As per our guideline we are supposed to answer only one asked question.kindly repost other question.…

Q: Show that if AB = AC and A is nonsingular, thenB = C.

A: Given that  A is invertible matrix. It means inverse of A matrix is possible. A is non-singular…

Q: 12. What can you conclude from (PV Q) ^ ¬P? Prove it.

A:

Q: Prove that AABC A DEF. C=12. D2,4) E(4, 2) 6-14.214 A6 4)

A: Compare the lengths of both the triangles.

Q: Given: 23 = Z1 Prove: АВ АС 2 3/6 E

A: Given: The angle ∠3 is equal to ∠1. Concept used: If the two angle of a triangle is equal then side…

Q: 2- Show that: (-1)m (2m + 1)! NIE

A: Solution:     Definition of Bessel's function:

Q: 3. Prove that {12a + 4b |a, b e Z} = {4c\c € Z}.

A: as per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: Compute AB, where A AT B = = 24 09 4 -3 -1 and B = 76 (1 %). 6 4

A:

Q: 5. Prove that arg(z1zz) = argzi – argzz %3D

A: Introduction: For a complex number z=x+iy, where x is the real part and y is the imaginary part,…

Q: 11. What theorem is used to prove that BD 1 AC? C В. D A

A:

Q: 1. • If r + 1| < o, prove that |r³ + 1| < 0.331.

A: Here we use the fact  | x |&lt; a implies  -a&lt; x &lt; a .

Q: 1S prove that (a + b) = a² + b².

A:

Q: Prove that for all a, b, and c e Z, if a † (2bc+12), then a † (b – 2) or a ł (c + 3).

A:

Q: BC = a. Prove: AB = 2a and AC = aV3. %3D %3D

A:

Q: If ZH and LJ are supplementary in HJKL, are a) ZK and ZL necessarily supplementary also? b) ZH and…

A: Given :∠H and ∠J are supplementary…

Q: 4. Let A C BCR. Prove A° C B°.

A:

Q: Prove that, if (a%m)=(b%m) then m| (a-b)

A:

Q: Prove this: A≤B iff AnB=A

A:

Q: Prove BCスツ+)B[スかリック =B(X1y)

A:

Q: 3. prove that: det (AB) = det (A) det (B) a - (; ), » - ( ) 2 -1 7 2 B = 2 в 3 %3D

A:

Q: Prove by contradiction that if m, n € Z, then m² - n is even or m-n-1 is even.

A:

Q: 11.32 question attached. Thank you for answering my question!

A: It is given that X and Y are independent normal random variables.The required probability is:

Q: 49. Prove that (a – b) × (a + b) = 2(a × b).

A: The following properties of vectors are used in proving the given identity. a×a=b×b=0a×b=-(b×a)

Q: 3. Suppose a, b, c E Z. Prove that if a? + b = c²,, then a is even or b is even.

A:

Q: Prove that OfVg.dr = ] (Vfx Vg) · N ds.

A:

Q: Show that: If |z| = 2, then: z* – z2 – 4| Re < 6 z + 6

A: A complex number z=x+iy are graphically represented as (x,y) on coordinate plane. The polar…

Q: (b) Prove or disprove that det (ABCD= det(A)det is jaett Jaet(D)

A: Let A=1111,B=1221,C=1332,D=1212 Therefore the determinants of individual matrices are: A=0,B=-3,C=-7…

Q: Prove indirectly: "V n E Z, 4 ł (n² – 2)."|

A: Ans:Let us assume that 4/n2-2;∀n∈zthen we have there exist a positive integer k such…

Q: Show that ∗ : R × R → R defined by        a ∗ b = a + 2b is not commutative.

A: Show that ∗ : R × R → R defined by        a ∗ b = a + 2b is not commutative.

Q: 2. Verify that det(AB)= det(A)det(B) and determine whether the equality det(A+B) = det(A) + det (B)…

A: Note : As per the authoring guidelines, when multiple questions are posted, then only first question…

Q: p) Prove that if ac | bc and c +0 then a | b.

A:

Q: 53. Suppose that a + 0. (a) If a · b = a·c, does it follow that b (b) If a X b = a X c, does it…

A: Given a, b, c are three vectors and a ≠ 0.

Q: 7. Establish for A is m × n and B, C are n x p, that A(B+C) = AB + AC

A:

Q: 6. Prove that, if a, b e Z, then 3a? – 4b – 5 0. - -

A: Answer

Q: 4.2. Let a, b € Z, where a + 0 and b + 0. Prove that if alb and bla, then a = b or a = -b.

A:

Q: 3. Prove or disprove: If a | (b + c), then either a |b or a | c. h of the follo

A: Since you have asked for question number 3 , we have solved it for you.

Q: Suppose n (a)= 7a + 4, determine a such that n (a) = 39. %3D

A: GIVEN n(a) = 7a+4 and n(a) = 39

Q: prove that a(a+b)=c(c+d). a b d

A:

Q: ) Evaluate, using Cauchy formula C:2- (a) zz-l dz dz (6) ( e

A:

Q: Prove this: A=B iff A° U B = Ω =

A: Solution : First prove left to right, If A⊂B is true , All elements of A are inside B, Then Ac is…

Q: Q1: Prove that ; If CE AB, D E AB and C# D, then CD = 2 %3D

A: Key point: 1. There is only one line possible from two distinct points.2. The line is expressed in…

Q: 3.1 Prove: For all a and B in R, Ja + B] > | |a| – |B||. Hint: la + B] = |a – (-B)|-

A: Answer is in below steps.

Q: 3. Prove that (An B)² C A x B.

A:

Q: I find B such that AB = C. If 5 0 3 A = 2 01 9. C = 3 5 c- (* :)

A:

Q: 4. Show that: do Tb/(a? – b²) - a+bcos0 а b2 Where a>b>0 such that * -1+ 1. < 1 - a²

A: To Show: ∫0πdθa+bcosθ=πba2-b2 Concept: i. 1+tan2x=sec2xii. cos x=1-tan2x21+tan2x2iii.…

Q: Prove the following:  if x^2 = y^2, then x = y or x = -y.

A: Subtract y^2 from both sides.

Q: Show for Re(z) > 1 -dr = r(2) ((2). %3D et - 1

A:

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.  

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.