Find (a) projvu and (b) projuv. Use the Euclidean inner product.u = (5, −3, 1), v = (1, −1, 0)

Q: Use De Moivre's theorem to find the following: 4 i. [1+ v3i]" -3 ii. [-1+ v3 i]

A: Given that: i. [1+3i]4 ii. [-1+3i]-3

Q: se the inner product (p, q) aŋbo + ajb1 + az p(x) = 3 – x + 2x², q(x) = x – x2 (a) (p, q) (b) ||p||…

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Q: 21) Find the area of a triangle fosmed from the twovectors a = L'+2j-k-.

A: Given, a ⇀=i+2j-kb⇀ =2i-j+4k

Q: Q: Show that the functi on f:R →R given by f (x) = ax +b, where ab e R, a #0 is a bijection.

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Q: Prove the product rule by use of ΔA=w⋅Δh+h⋅Δw+Δw⋅Δh

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Q: Compute the orthogonal projection of onto 7. Use the square root symbol 'V' where needed to give an…

A: Given u→ = -996,  v→ = 1-1-1

Q: nd A’A and AA'. -1 1 4 A = 2 0 2 (a) ATA (b) AAT 18 6 hich of the products are symmetric? (Select…

A:

Q: Consider P2 with the standard inner product. Then which one of the folloWing pair is orthogonal a)…

A:

Q: Find (u, v), u, v|, and d(u, v) for the given inner product defin u-(-5,4), v = (0,-2), (u, v) = 3u…

A:

Q: Write a two column proof. Given: AN//GR, AG bisects NR Prove: AAXN = AGXR A

A: This question is based on Congruence of triangle.

Q: is bijection. Do the same thing with Z,.

A:

Q: Verify that the operation {x, y} = x1y1 − x1y2 − x2y1 + 3x2y2 where x = (x1, x2) and y = (y1, y2) is…

A: Given : The operation on ℝ2 is defined as  x, y = x1y1 - x1y2 - x2y1 + 3x2y2 ,  where x = (x1 , x2)…

Q: Q.4.(a). Show that the following functions is not an inner product on R3, where u = (u, U2, U3) and…

A:

Q: Find (a) projvu and (b) projuv. Use the Euclidean inner product.u = (1, 2, −1), v = (−1, 2, −1)

A:

Q: Consider P2 with the inner product given by evaluation at - 2, 0, and 2. Compute ||p|| and |q| for…

A: In this question, concept of inner product is applied.

Q: Find (a) projvu and (b) projuv. Use the Euclidean inner product.u = (−1, 4, −2, 3), v = (2, −1, 2,…

A: Given:

Q: Let v = Does {v1, V2, V3} span R*? Why or why not?

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: True or False: (p, q) = pq defines an inner product on P(R).

A:

Q: Find the norm of (-4,- 1/4,3, 1/3) belong to R^4 w.r.t the Euclidean Inner Product on R^4.

A:

Q: Let R' have the Euclidean inner product and let u = (1, 2, -1) and v = (3, 1, 0). Then proj u 5 10 6…

A: Let IR3 have the Euclidean inner product space and let u=91,2,-1) and V=(3,1,0)then projuu

Q: Give an example of (v1, v2, v3) and (w1,w2, w3) independent se- quences in the Rº such that…

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Q: ® Use the inner product (u,v> = 24, Vi +Uz Ys and the Gram- Schmidt orthonorma lization trow foom…

A:

Q: LetV = K". Show that V with the usual dot product is a scalar product. %3D

A: (1) Given that V=Kn If V with the usual dot product. So, for any x in V,…

Q: Let R have the Euclidean inner product. Let u (1, 1, -1) and v (7, 6, -15). If ||ku + v|l= 7, what…

A: A vector is a quantity that has both magnitude and direction. It can be also defined as the…

Q: Find A'A and AA". -1 1 4 A = 2 0 2 (a) ATA (Б) ААТ Which of the products are symmetric? (Select all…

A:

Q: Explain why is not an inner product for u =(u1, u2) and v =(v1, v2) in R2 when = u1u2 + v1v2 using…

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Q: Respond as indicated 1.) Find the norm of u=(5,6,1) with the respect to the usual inner,product (dot…

A:

Q: Consider R' endowed with the dot product. Let W = span{u1, u2} where u1 = (1,0, 1) and u2 = (-1, 1,…

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Q: Find the resolvent kernel and Solut of ya) = I+5(1-3x+).y(t).d by Alternative procedure

A: Given Integral equation is y(x)=1+∫01(1-3xt)y(t)dt               (1) The general form of integral…

Q: Show that the function does not define an inner product on R3, where u = (u1, u2, u3) and v = (v1,…

A: For satisfying the inner product condition, function has to follow these three conditions: 1)…

Q: (bj) be the squar %3D E i, j< 3. If the detern nt of BT is

A:

Q: Use the inner product (f, 9) = f(2)g(=) dæ in the vector space P(R) of polynomials to find (f, 9),…

A: The inner product is f, g=∫01 f(x)g(x) dx The functions given are f(x)=10x2-3 and g(x)=-9x+10

Q: If Z=1//2+j/v2 then the value * ?=of conjugate of Z^5

A: According to Euler, the complex number of the form cosθ+isinθ can be written as eiθ. The conjugate…

Q: Let R' have the Euclidean inner product and let u = (1,-2,-1) and v = (3, 1,0) Then proj, u %3D

A: AS PER GUIDELINES I HAVE SOLVE ONLY FIRST ONE

Q: (b) Are the polynomials x + 5, x – 5, 2x +1 linearly independent in P1(R)? Explain.

A: The vectors a1, ..., an are called linearly independent if there are no non-trivial combination of…

Q: Let r (t) = The dot product r (1) · r ' (1) =

A: First differentiate at given value then take dot product

Q: R. find he Corficient of

A: We need to find coeffiient.

Q: In RX1, let U = span ( 1 Find bases for U- and (U-)+.

A:

Q: Show that the function defines an inner product on R3, where u = (u1, u2, u3) and v = (v1, v2, v3).…

A:

Q: Supbose A, B and c in vestible matnices , show also invertible AB C is that by baioducing matnix D…

A: Let A-1, B-1 and C-1 denotes the inverses of matrices A, B and C, respectively.Show that ABC is…

Q: 3] By using the properties of dot and cross product, prove the following: a) (w x ū). ū = 0.

A: To prove- w→×v→.v→=0 The cross product of two vectors…

Q: Find p|| and d(p, q) relative to the standard inner product on P2. p = 11 - x + x², q = 7 + 9x² lll…

A: We have given p=11-x+x2, q=7+9x2 Then, p=11-x+x2=112+-12+1212=121+1+112=123

Q: And a. he minor of the element in the i li, ro Column of ass the deferminant of A, find

A:

Q: In ABCD, AB = BC = CD = DA. Prove that AC and DB bisect each other at right angles. Use two-column…

A: We have to prove that AC and BD bisect each other at 90°

Q: Show that the function defines an inner product on R3, where u = (u1, u2, u3) and v = (v1, v2,…

A:

Q: Use the inner product (А, В) — 2а11bi + az1bz1 + aj2b12 + 2а22b22 to find (A, B) for A = -1' B = 4…

A: Question from linear algebra.

Q: Using Euler’s formula but not using Kuratowski’s Theorem, prove that K5 and K3;3 are not planar.

A: We need to prove K5 and K3,3 are non planar graphs. For that we must use Euler's formula. The…

Q: Find (a) projvu and (b) projuv. Use the Euclidean inner product.u = (0, 1, 3, −6), v = (−1, 1, 2, 2)

A: If u=a1, b1, c1, d1  and v=a2, b2, c2, d2 are two vectors, then projection of u onto v is given by:…

Q: Let R' have the Euclidean inner product and let u = (1, 2, –1) and v = (3, 1, 0). Then proj u

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Q: Calculate the scalar triple product u · (v x w), where u = (7,7,0), v = (-3,–9,7), and w = (7,–9,…

A: