o Let ã = (5,-2,-2) and 5= (-3, -3,0) ニ Show there ane scalars s and t so that -> sá + tb = - E22,-8,4) t

Q: 4. Two uniform vector fields are F = 2a, +3ā, -5ä,. Find ExF. given by E=-3a +5ā, +2㸠and

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Q: Let C := {1, cos t, cos 2t, . , cos 6t} C V where V is the vector space of all real-valued functions…

A: Given: C:=1, cost, cos2t,…,cos6t⊂V. V=f | f:0,2π→ℝ is the Vector space. J=spanC To prove: C is a…

Q: Find a basis for the plane 4 + 3y + 5z = 0 in R. %3D

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Q: Let B = {v1,..., Vn} be an orthonormal basis for R". (a) Prove Parseval's Identity, that is, for any…

A: According to the given information,

Q: the coordinates of (2, 3, 4, – 1) with B = {(1, 1, 1, 2), (1, –1, 0, 0), (0, 0, 1, 1), (0, 1, 0, Q}}…

A:

Q: 4 -2 -2 Let y = = 'n: -6 In -9 -2 Compute the distance d from y to the plane in R' spanned by uj and…

A: given  y=29-9 , u1=4-2-2 , u2=-22-6 compute the distance dfrom y to the plane in ℝ3spanned by u1 ,…

Q: (a) Prove that if u is orthogonal to both v and w, then u is orthogonal to v + w. (b) Prove that if…

A: Given: (a) If u is orthogonal to both v and w. To prove:  u is orthogonal to v + w. (b) If u is…

Q: Find non singular matrices P and Q such that PAQ is normal form 1 23 1. Ans. p= Q=0 [31 2 5 0 0 1

A: The given matrix is, A=1233122×3 Since A is of order 2×3 so pre-multiply by I2 and post multiply by…

Q: b) If a mass mis placed at the end of a spring, and if the mass is pulled downward and releas ed,…

A: The mass-spring system is oscillated when the mass m is pulled down. The displacement, of the mass…

Q: 8. Let x and y be vectors in 3-space, and suppose u is orthogonal to both x and y. Prove that u is…

A: Let x and y be vectors in 3-space and suppose u is orthogonal to both x and y  This implies  < x,…

Q: Is this the basis? What is the rank of A?

A: According to the given information, it is required to find the basis and rank of matrix A. The…

Q: a. The zero vector 0 is in ker(A) b. If x and y are in ker(A), then so is z = x + y. c. If x is in…

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Q: a) Let D be the differential operator on the vector space P2(R). Given two ordered bases a = (1, x.…

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: 3.2.14. Fix 1 <p< oo. Given x, y E lP, prove that ||r+ yllp = ||x||, + ||y||p if and only if x = 0…

A: Let x,y∈lp where 1&lt;p&lt;∞. Suppose x=0, then x+yp=0+yp=yp=0+yp=xp+yp Suppose y=αx, where α is a…

Q: QUESTION 4 Let V be a vector space of dimension 2n > 2 over R. (4.1) Show that a complex scalar…

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Q: Which are eigenvectors of the operator S:R^3->R^3 defined by S(x,y,z)=(y+z,x+z,x+y) ? Check all that…

A:

Q: show that vectors Centywhere en I's the sequence whose nth term i's 1 and all o ther terms are Zero…

A: Given: The vectors en where en is the sequence whose nth term is 1 and all other terms are zero.…

Q: EX ample (12.1) Find the Singular Value De composiion of A= 0 4 3 4 00 3 00 Solution: FInd Q2…

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Q: Let C := {1, cos t, cos 2t, cos 6t} C V ...) where V is the vector space of all real-valued…

A: The given set is C=1,cost, cos2t, cos3t, …, cos6t⊂V. Where V is the vector space of all real valued…

Q: Let uj = (1,1,2), uz = (1, 3, –2), Uz = (4, –2, –1) in R’. Show that u , U2 , Uz are orthogonal, and…

A: u1=112,  u2=13-2,  u3 =4-2-1 vectors are orthogonal if their dot product is zero  . u1·u2=11213-2…

Q: H.W. 2 Let 71 = -2 + 1li, 22 = 2 - i. Showing the details of your work, ind, in the form x + iy: %3D…

A: z1 = -2+11i z2 = 2-i (z1 - z2)2/16 = (-2+11i -(2-i))2/16 = (-4 + 12i)2/16 = (16 -96i -144)/16 (z1 -…

Q: Show that UE span{(1,2, – 1,0),(1,1,0,1),(0,0, – 1,1)} where u= (2,5, – 5,1) by finding scalars k,I…

A: We have,u=2,5,-5,1andu=k1,2,-1,0+l1,1,0,1+m0,0,-1,1---1

Q: 6. Determine the number of zero's for h(z) = 2z* – 3z² + 2z – 5 inside the disk |z| = 2. (Use…

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Q: b) If a mass m is placed at the end of a spring, and if the mass is pulled downward and released,…

A: Solve according to fiven question

Q: Which of the centroid(s) are trivial

A: Note that : A region if is symmetric about y-axis then x-coordinate of the centroid of the region is…

Q: Suppose u = (5, 3,0), v = (0, 3, 9), and w = (-1, –9, –3). Compute the three triple scalar products…

A: We will solve the following.

Q: Let u = &lt;1, 2, 1&gt; , v = &lt;1, -1, -1&gt; , w = &lt;1, 1, -1&gt; , and z = &lt;2, -3, -4&gt; .…

A: Given vectors

Q: ey are linearly dependent, find scalars a, b, and c, not all zero, such that au + bv + cw = 0 u =…

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Q: 21 AATC has vertices at A(-8, -5), T(8, -5), and C(4, 1). Determine the coordinates of the centroid.…

A: The formula to find the coordinates of centroid of a triangle having vertices x1,y1, x2,y2 and x3,y3…

Q: Let uj = (1,1,2), uz = (1,3, –2), uz = (4, –2, –1) in R’. Show that uj , uz, Uz are orthogonal, and…

A: The answer is given in this below photo

Q: If f(x) = x^2 + 7x+2, g(x) = x^2 - x + 1 find a polynomial h(x) of degree 2 such that together these…

A: Given:  f(x)=x2+7x+2,g(x)=x2-x+1 We have to find a polynomial hx of degree two such that together,…

Q: 8. [M] Show that {1, cos t, cos? t,..., cos t} is a linearly inde- pendent set of functions defined…

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Q: 10. Consider the plane 2x - 3y+4z 0. Find a basis B of this plane such that (B = for ū =

A: Solution:-

Q: 4.13 Let {u1,u2,..., un} be any orthonormal basis of (where F R or F = C). Show that %3D Euju; = 1.…

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Q: Find u x v where 1) u = (4,3,6) and v = (2, 5, -3). u = (1,-1, 1) and v = 2) (2,1,0), 4) u = i+jcos…

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Q: 1 Q.2) How can you show that the set{ 2 2} form basis of xy- plane in R3? 3

A: GIVEN SETS : The given sets are : 120,123 The augmented matrix is : 120123R2→R2-R1~120003

Q: 1,3x-2 4. Determine whether the veltors X-I and X²-3x+2 dve lihearly independent or dependent in Pz…

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Q: Let P be a 2 × 2 orthogonal matrix such that ∣P∣ = 1. Show that there exists a number θ, 0 ≤ θ &lt;…

A: Here it is given a matrix P and determinant of P.

Q: Let B'- {1+2x, 3-x} And B = {1,x} be Basis for Pi a) s Find the Transilion matrır Pine from B' toB…

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Q: /- X be the vector Space of all Complex 2x2 and de fine T: x →x by Tx = bx, where Let matrices bEX…

A: Given :-  Let X be the vector space of all complex 2×2 matrices and define T : X →X  by Tx = bx ,…

Q: Q: Find a representation of Jp(t)> at a time t +0 using the ordered basis {|e1>, ]e2>, ]e3> }.

A:

Q: -3 6 8. Let ū = = and w : Is it possible to find a scalar t such 1 -3 -4 that ū + tỉ is parallel to…

A: Given that,  u→=-321, v→=50-3,  w→=61-4 And  u→+t v→ is parallel to w→. To find the value of scalar…

Q: 1. Let R? have the inner product of Example 1, and let x = (1, 1) and y = (5, – 1). a. Find ||x||,…

A: Let R2 have inner product s.t.if u= u1,u2 and v=v1,v2 betwo vectors in R2then &lt;u,v&gt;=u.v…

Q: 6. Define fe (R2)* by f(x, y) 2x + y and T: R2 (3x + 2y, x). (a) Compute T'(f). (b) Compute [T']p,…

A: We will use the basic knowledge of linear transformations to answer all the three given subparts of…

Q: Consider the following. {(-1, 2), (6, 3)} (a) Show that the set of vectors in R" is orthogonal. (-1,…

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Q: If x, x is a basis of solutions of r'y" + ary'+ by = 0, %3D then a = (A) -2 (B) 2 (C) -3 (D) 3 (E)…

A: Just use definition of solution of differential equations.

Q: 2. 5. Consider twO basis of R: B = %3D -3 and (= 3. 5- 1- with respect to B, If a vector V E PR has…

A: The given 2 bases of ℝ2 are as follows. B=75, -3-1 and C=3-5, -12 Also, the coordinates of the…

Q: show that a set of vectors{et cos(2t), e¯t sin(2t)} form a basis of solution space for x" + 2x' + 5x…

A: Substitute the value of x in the solution space and see if the value satisfies the equation, if the…