WPITE THE しINEAR FQUITIONSMAKE GRAFUS 2) , w-2 3) (x,)=4,), ()- -1) +) =,9), )-6) 5) (0M)=7,3))- (3) )=3,1)

Q: O Prove that Q(Vationalnumber bers)is negrigibleset

A: This follows easily from the definition of a negligible set. We recall the definition and present…

Q: described

A:

Q: Show that a fomws with R>o Ssee igue] may be descuibed panometuicaly by u cU,N] Cosu, (R+ o…

A:

Q: 2. Prove that if two straight line segments r and r'are parallel transports another straight line L,…

A: Consider the equation

Q: Find diagonal matriy D is similar with A a A = [3 8-5

A:

Q: Prove that the four points P(2, ;1, 1), Q(1, 3, ; 2), R((2, 1, ; 3) and S(3, 2, 0) are coplanar

A: Given four points are  P(2,1,1)Q(1,3,2)R(2,1,3)S(3,2,0)

Q: 25. Show that |v|u + Ju|v and |v|u – |u| v are orthogonal.

A: Two vectors are orthogonal if their dot product is zero. If the dot product of two vectors is zero,…

Q: 4, Find the difence eten he um f thefist the consecutie intgear frm -2 and the sum of hefist for…

A: here 3 positive consecutive  numbers  2,3,4 and  3 consecutive numbers from -1 are -1 ,-2,-3,-4

Q: prove that 2. catX+c

A: We use that- sin2x + cos2x =1  so that 1-cos2x= sin2x

Q: ) Find the fomily of the equ ation of all lines in 3-space perpen diuler to 2x -y +2u u Given line

A: Family of lines contains parameters.

Q: Suppose that receiving stations​ X, Y, and Z are located on a coordinate plane at the points…

A: Given that receiving station x = (15,7)   ,  y = (-9 , -3) &   z = (-9 , 7)Now, let coordinate…

Q: we divesgencatheosem to evaluate + XzK. dA cohose sisthe boundasy of cube definedd by

A: By divergence theorem we convert the given surface integral to the volume integral, and the region…

Q: In AHIJ, HJ is extended through point J to point K, mZJHI = (x + 12)°, mZHIJ = (x - 3)°, and mZIJK =…

A:

Q: (i) (Z- Q) and specified in it using the most concise notati

A: Firstly we write elements of both sets Z and Q and then find Z–Q

Q: 3) Use Green's Theorem to evaluate o-ydx+xydy where C is the line segment from (-2,0) to (2,0) then…

A:

Q: A, is skew-symmetric, then prove that (B B + B, B') An = . Ajk = 0. %3D

A:

Q: What is u × w, assuming that w × u = 〈2, 2, 1〉?

A: Given,w×u=2,2,1 To find:u×w Solution: We know ,by property of cross product of two vectors (say,a…

Q: 3. Show that B = {0, 1, 2, 6, 9} is a difference set in Zjj. What are the parameters of the SBIBD…

A: For the given question ,t he first thing to do is to find the value of λ. Then, we will proceed…

Q: 5. If r = (r, (x, y, z) and ro = (xo, Yo, 20), describe precisely the set of all points (r, y, z)…

A: We plug the given values in the given equation and simplify

Q: find the fimet Qurtal dernratives 7 respect to rarraes X,4,Z.

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: Find oxthogonal uncdary diagonalizing an or matri'y to lMowing tor One 2 (a) (b) 3 -2 -2

A: A square matrix A is called as orthogonal matrix if AxAT=ATxA=I where AT transpose of matrix A. and…

Q: Con sider Sam ple X,, X2,.., Xg from a NC8,4). Find the Coverage Probabilit a of interval [x-2, +2].

A:

Q: Where does et tanget line - Bx* Have a harizontal a hor:zontal

A: Given:- y=ex^4-8x^2  To find:- Points where tangent are horizontal

Q: 8. Show that, for u, v E R³, ||u|| ||| = (u - v)² + ||u x v||².

A:

Q: Hew.b prove that CAXB)-Ais atways-Zero

A: Topic:- vector  algebra

Q: Prove that MSE(Ô) = V (ô) + [Bias(Ô)]²

A:

Q: 1. What congruence postulate/theorem cannot be used to prove that ALIV AJIN given that LVis parallel…

A: topic- congruent triangles

Q: Show that R³ is spanned by S = {(1,1,1), (1, –1, 0), (0, 1, – 1)}.

A:

Q: Show that R³ is spanned by S = {(1,1,1), (1, – 1, 0), (0, 1, – 1)}.

A:

Q: Let A be a 7*4 matrie. What must a and b in or der to TO= Ax?

A: For it to be possible that two matrices A,B  can be multiplied as AB then we must have number of…

Q: Prove that if A is skew-symmetric matrir, Q = et is orthogonal.

A: c) To prove:- If A is skew-symmetric matrix , Q=eAt is orthogonal. Proof:- Ais skew-symmetric matrix…

Q: show that d connot be obtained from a norm.

A:

Q: Let it be S={ ujuP alinearly in dePendent SEl

A: # As per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: (3) In R² with the standard topology: {(x, y) | x² + y² {(x, y) | x² + y? > 1}. = 1}, {(x, y) | x² +…

A: In a topological space R2with standard topology. A  subset O is open if at each point x in O there…

Q: /prove the fottowing Eoshlutv)= Coshucoshv+ Sinhu Sinhk

A:

Q: Let Flx,4z)=xi-zsinluzljtusinlyalk. Colculote é Fdr, where cis a path from A:10,0,1) +o B-13,1,2)

A:

Q: Compute ∮c (ydx+zdy+xdz) where C is the triangle with vertices (3,0,0), (0,0,2), and (0,6,0)…

A: The given points can be plotted as A(3,0,0) B(0,0,2) C(0,6,0)

Q: Show that U. AS cuhere N= {3 unaluralnun %3D

A: To proveG={N,*} is not a group under binary operation a*b=ab where a,b∈N

Q: 2) Prove by using the pigeonhole principle that among any 17 points in a square of side one there is…

A: Given: A square of side one contains 17 points. To show: There is at least a pair whose distance is…

Q: Let A=(aij)nxn be symmetric and positive definite. Show that laul< (anan), , lis = 1,2,..n 9

A: Given: Let us consider the given, A=aijn×n Let's prove that aij&lt;aiiajj12,i,j=1,2,...,n.

Q: By using Cauchy Residle Theorem 到一2p 121=1

A: First we have to find residue at singular points.

Q: 2) Evaluate yzdx+ xzdy + xydz where c is the line segment from (1,1,1) to (3,2, 0).

A: Given: c is a line segment joining 1, 1, 1 and 3, 2, 0. To evaluate: ∫cyzdx+xzdy+xydz

Q: Show that R3 is spanned by S = {(1,1,1), (1, –1,0), (0, 1, – 1)}

A:

Q: In AJKL, JL is extended through point L to point M, MZLJK = (x + 9)°, mZJKL = (x - 2)°, and m/KLM =…

A: The exterior angle is equal to sum of two opposite interior angles. We will use this property to…

Q: (b) Show that when dist(x, y) = dist(x, –y), then x and y are onal. orthog- %3D

A: Given  dist(x,y) = ||x-y||

Q: 31) Find two sets af poler Coorelinates for tue pornt (0,-4) Jer OLQL2T Auywers's 37 テノ, (16,…

A:

Q: 7 Write the quackatie fundion anose nertex b (-2,5) and wise 4-int is -1 in Staniald foron

A: The quadratic function has vertex -2,-5 and whose y-intercept is -1

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.