Theorem 11. Let A E Mn be positive semidefinite . Then A has a real root. Moreover ,the square root can be choosen to be positive

Q: Prove that if A is invertible and AB = 0, then B= 0. Give a counterexample to show that the result…

A:

Q: If W(-10, 4), X(-3, -1), and Y(-5, 11) dassify AWXY by its sides. Show all work to justify your…

A: Given,           If W-10, 4, X-3, -1, and Y-5, 11 of ∆WXY.

Q: Let S,T,U E S(V). Show that if UC S, then Sn(T+U) = (SnT)+U %3D This is called the modular law for…

A:

Q: Use Euler's method to obtain a four-decimal approximation of the indicated value. Carry out the…

A:

Q: Find the dimensions of the minimum-cost open-top rectangular tainer. (Let v* = 10 m³.) con-

A: Given. We need to find the dimension of a topless cuboidal container. Whose volume is 10m³ And…

Q: Consider the paraboloid paremterized by o(u, v) = (u, v, u² + v²). 1. Find the second fundamental…

A: 1 Consider the paraboloid parameterized by σu,v=u,v,u2+v2. We have to find the second fundamental…

Q: Find the conjugate of z = -2 – 4i, and compute zz. z = zz =

A: Given that: z=-2-4i

Q: 4) Use Green's Theorem to evaluate f √1+x³dx + 2xydy. C is the triangle with vertices (0,0), (1,0),…

A:

Q: 1. Let points A, B, C be located as shown in Figs. 4.11 and 4.12. Construct the harmonic conjugate…

A:

Q: 4. Exercise §5.2 #20 [This exercise presen Theorem 5.9 using the Möbius Inversion Form to that in…

A: Given, d be a positive divisor of p-1. To prove that                            f(d)=ϕ(d)

Q: Show that if A is invertible and DA = CA, then D = C.

A: Given that, A is invertible and DA=CA.

Q: (a) Prove that if A is invertible and BA = CA, then B=C. (b) Give a counterexample to show that the…

A: Given:         Part(a):Since A is invertible then A−1 exist.Now,BA=CA(BA)A−1=(CA)A−1…

Q: Icm(a, b) = ab if and only if a and b are relatively prime. %3D ylgn O ihi O

A: True

Q: (5). If A, B and A+B are each non-singular and the products are conformable, prove that (a). A(A +…

A:

Q: #2. Find invertible matrxes B and C SO C M.B =

A:

Q: 8. Work out a Gaussian quadrature formula of the form Ans. A; = 1, x; = Aif(x1) + Arf (x2). f(x) dr

A: The given problem is to prove the following integral, the proof is to show the 2 point gaussian…

Q: 4. Show that the norm on (° given by I| (21, ..., In...) |lo= sup{|7;| : j =1,2, ...} %3D can not be…

A:

Q: Prove that if A is invertible and BA = CA, then B = C.Give a counterexample to show that the result…

A: Given: A is invertible and BA = CA  To prove: B = C

Q: Find the residues of each of the fellowing functièns at its. poles. e •f(z)- 22+3 4. ans : ri=7/4 ?…

A:

Q: Let z2T3-L p=S+Si O fird all the complex mumbers %3D guien by hza

A:

Q: graup Consider a dibedral 2. Du= carb: d=b-(ab)"%=D1> Discuss all passible Commulators 'and verify…

A:

Q: where A e C.

A: Complex Inner Product Space: For two vectors u and v in complex space ℂn, u,v is known as complex…

Q: A natural cubic spline S on [0,2] is defined by |So(x) = 1 + 2x – x³, S(x) = if 0<x< 1, |Si(x) = 2 +…

A: Given Sx=S0x=1+2x-x3if 0≤x&lt;1S1x=2+bx-1+cx-12+dx-13if 1≤x≤2

Q: @ Let A -a Find Cenditiens on a,b.c and d that AX =o has infailely many Solution. what must there…

A:

Q: A natural cubic spline S on [0,2] is defined by (So(x) = 1+ 2x – x³ S(x) = Is, (x) = a + b(x – 1) +…

A: Given: Natural cubic spline S on [0,2] is defined as: Sx=S0x=1+2x−x3 if 0≤x≤1S1x=a+bx−1+cx−12+dx−13…

Q: Which gralf shows only a rotation of 180 about the orgin of square JKLM to square J'K'L'M'

A: In the first two graphs, the rotation is not about the origin but it is about x axis. hence, none of…

Q: Show that following MA models are equivalent A: Yt = et – Oet-1 for et ~ WN(0, 1) 1 Yt = et for et ~…

A:

Q: O consider A= 2 2 3 is A Diegnalizatle? if yes cateulate the dognal matrin D and invertible malyix P…

A:

Q: Solve the followig 13. BauSsian or Eduss Jordan Using E lemination. 5x, +6x=7X 3D0 3. ース×,+ 3X7…

A: Answer

Q: Let A ∈ M nxn(F). Show that A is diagonalizable if and only if At isdiagonalizable

A:

Q: Let a < c < b and s(x) be a cubic spline with a single node c. Suppose s(x) = 0 on [a, c]. %3D Show…

A: Let a&lt;c&lt;b and sx be a cubic spline with a single node c. Let us consider sx=0…

Q: Theorem 2.6.9. If P and Q are two points such that P + Q, then there exists a point R such that P,…

A: Axioms used: 1. There is one and only one line that contains two distinct points. Given: Theorem…

Q: Find the projection of b = 5i – k onto à = i+ 2j+ 3k. %3D

A: We have to find the projection of →b on →a

Q: Let A,X EM, (C) such that A is positive semidefinit and AX = XA Show that A¹/2X = XA¹/2.

A: Introduction: Definite matrix is significant in studying quadratic forms. Also, in Lyapunov…

Q: In real-number multiplication, if uy1 = uy2 and u ≠ 0, we can cancel the u and conclude that y1 = y2…

A: Given:

Q: a let a bereal number . Explan why the planes x + 2yf az = || and ax + 2y +az =17 are uot orthogonal

A: if plane are orthogonal then cos x = 0

Q: -3 [-1+v3i]

A: Explanation of the answer is as follows

Q: (c) Prove, by induction on n, that for all n, a product of n fundamental unit quaternions represents…

A: To prove that, by induction on n, that for all n, a product of n fundamental unit  quaternions…

Q: 7. Trapezoid ABCD has bases AB and CD. If AC and BD intersect at X, then AAXD and ABXC are ?…

A: Given: Trapezoid ABCD with bases AB¯ and CD¯ and  AC¯ and BD¯ intersects at X. To determine: ∆AXD…

Q: Describe the tronsformaton that must be performed, On the of y=&5)*-3 gaph of y= xh to Obtuin the…

A:

Q: Complex Analysis

A: For given function, First we will show the function is harmonic function as shown below :From the…

Q: Factor 11 + 3i in Z[i] into indecomposable Gaussian integers. Hint: use the norm to guess factors.

A: Using the norm to guess the factors.

Q: Prove that (A+B)T=AT+BT

A:

Q: Show that if B is m × n, then BTB is positive semidefinite; and if B is n × n and invertible, then…

A:

Q: 1 Let A= -2 . Show that A is positive semidefinite and find A2 4

A: Given the matrix is A=1-2-24. Show that A is positive semidefinite and find A12.

Q: Prove that if A is invertible and AB=0, then B=0.

A: Given:

Q: A natural cubic spline is defined by [a, (x – 1)' + b, (x – 1)² +c, (x – 1) + d, f(x) = if 0<x<1 (x…

A:

Q: a) Show that u(x,y) = x3 – 3xy2 + 3x2 – 3y2 is harmonic and find its harmonic conjugate

A:

Q: In the space referred to a direct orthonormal system ( O; i, j, k), given the points A (6 ;4;-7) ;…

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.