4 1 R2 generated by A = 4 -3 and let u = (4,-3), v = (-3, 3). Let (u, V) be the inner product on %3D Find (u, v). (u, v) = %3D -21 Edit

Q: Find div F and curl F if F(z, y, z) = 9e#i-9 cosyj+3sin? z k. %3D div F = curl F=

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Q: Current Attempt in Progress Let R3 have the Euclidean inner product. For which values of k are u and…

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Q: Find the matrix of T(x, y, z) = (3x, -6y) relative to the standard bases. T = Use this matrix to…

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Q: 12. The matrix that represents a reflection on the plane 2x – y + z = 0, is given (in the standard…

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Q: Find the standard matrix for the reflection T of R'in r= 21 the line {y=-t. Your work must be shown!…

A: The solution is below.

Q: 9-12. Locate the centroid F of the area. Probs. 9-11/12

A: Given equation  y=hx2/b2

Q: Find (u, v), ||u|l, ||v||, and d(u, v) for the given inner product defined on R". u = (1, 1, 1), (5,…

A: Given that, u=(1,1,1) and v=(5,2,5).

Q: is not diagonalizable (by similarity) but is condiagonalizable. 4.6.P2 Show that (a) [ (b) [] is…

A: To show: (a) The matix i10i is not diagonalizable but it is condiagonalizable. (b) The matix 1-111…

Q: 5. Find the three by three matrix A such that [r – y] A. y for all r, y, z in R.

A: In the given problem we have to find the three by three matrix A such that…

Q: Find the outer product form of the SVD for the given matrix. (Enter sqrt(n) for vn.) 5 0 A = 0 5 0

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Q: b. a Let A = If (x, y) = y" Ax defines an inner product on R? for all æ, y E R² , show that a + c >…

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Q: Let A denote the 2 x 2 matrix We define a function (, ) : R² ×x R² → R by taking (x, y) = y" Ax, for…

A: We have A=1221. We are given the function ·, · : ℝ2×ℝ2→ℝ by taking x, y=yTAx, for each pair of x,…

Q: Let A denote the 2 x 2 matrix 2 We define a function (•, ·) : R² × R² → R by taking 1 (x, у) %— уТ…

A: We have A=1221. We are given the function ·, · : ℝ2×ℝ2→ℝ2 by taking x, y=yTAx for each pair of x,…

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…

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Q: (E)-L) 2x1 Let T : R → R² be defined by T -3x2 + x3 0. 2 -6 Let B = { ui U2 = u3 and C = V2 = -6…

A: Solution:-T:ℝ3→ℝ2T:x1x2x3=2x1-3x2+x3B=u1=6-4-6, u2=017, u3=2-5-1C=V1 =76,V2=-64∴TBC  should be 2×3…

Q: Let x=x= and y=y= Find the dot product of xx and yy.     x⋅y=x⋅y

A: Given:x=9, 0y=-4, -2Dot product:A=ax ,ay  B=bx ,byAB=axbx,+ay,by

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…

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Q: Consider the bases B = {u1,u2} and B' = {v1, v2} for R² where 3 uz = 4). v. = (4). v2 = (G) U1 V, =…

A: Given :  The bases B = {(1, 0) , (0, 1)}  and  B' = {(2, 1), (-3, 4)} for ℝ2. To find : We have to…

Q: snip

A: u,v=4u1v1+u1v2+u2v1+4u2v2

Q: = (3, 6) 2. It is known that u = (-2,3) and v = relative to the inner product in R? which is derived…

A: 2 Given that u=−2,3 and v=3,6 And A=2134. We have to find the u and v. We know that…

Q: Day: Month: 23 3 : E = { c : LT] -> Buis absolutely continuous. Year: م ,C C C11 ,(1) = (0) c مردم…

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Q: (a) Use Green's Theorem to evaluate S. axy dx + cxy dy, where C is a counterclockwise oriented…

A: Given that , a=2 , c=5 Evaluate , ∫Caxydx+cxydy where C is bounded by x=-a , x=a , y=-c , y=c

Q: -2x1 Let T : R³ → R² be defined by T -3x2 + *3 x3 -3 and C = -5 V2 Let B = u1 U2 = U3 V1 = 7 ] =»}…

A: Given that T:ℝ3→ℝ2 be defined by Tx1x2x3=-2x1-3x2+x3.Let B=u1=-33-1,u2=-72-5,u3=6-47 and…

Q: Topic is inner product: given below, find (i) ||x|| , (ii) ||y|| , and (iii) x · y  b.  x = (1, -2…

A: given below, find (i) ||x|| , (ii) ||y|| , and (iii) x · y  b.  x = (1, -2 , 0 , 1) , y = (1 , 1 ,…

Q: P3 have the inner product given by evaluation -3,-1, 1,3 produce an orthogonal busis for P2 by…

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Q: = -2 + 11i, z2 = 2 – i. Showing the details of %3| | your work, find, in the form x + iy: Re (z).…

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Q: #9. Showing work, evaluate the following determinant by using the properties of elementary row or 2…

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Q: tan" (x)) Determime the giwen serves is convergent or duergent. Show and State the theorem/test ypu…

A: Answer and explanation is given below...

Q: be the bases in  R³ T={,,},     S={,,} determine the matrix of transicion of T to S

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Q: 5. Use the transformation u = x + y, v = x – y to find dA. - R Where R is the rectangular region…

A: Given integral  ∫∫Rx-yex2-y2 dAwhere  R is the rectangular region enclosed by the lines x+y=0   ,…

Q: (b) Evaluate f. F• dr by using Stoke's Theorem, where F = zi + xj + yk and C is perimeter of closed…

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Q: space of R3 spanned by S. 1, 3, 3), (1, 1, 1)} ed row-echelon form of the matrix whose rows are the…

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Q: Find w such that 2u + v - 3w = 0. %3D u = (-6, 2, 0, 0), v = (5, –3, 0, 1) w =

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Q: Let A, B. C, D and E be 3 x 3 matrices such that det(E) = 3 and: A R+ R B R R В C R3 → R3 -R2 D R→…

A: Effect of elementary row operations on determinant 1)Switching teo rows or columns causes the…

Q: 4)Determine the jacobian u = x (1– r²) i, v= y (1- r²) w = z (1 – r²) /hen r2 = x² + y2 + z2…

A: Given u=x1-r2-1/2, v=y1-r2-1/2 and w=z1-r2-1/2 where r2=x2+y2+z2…

Q: 3. * Find f -6xydA over the triangular region D with vertices (0,0) (2,0), (0, 4) -16 -8 -68 16 68 8

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Q: - 3 - 2 Let y = u2 = Find the distance from y to the plane in R' spanned by u, and u2. - 6 u = - 5 1…

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Q: Matrix A=(a)nxn is called strictly diagonally dominant, if "1 |a₁|> Σ |aj|, Σ |aj|, i=1,2,...,n.…

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Q: Consider the bases B= (u1, u2) and B' = {uj, u½} for R², where -[} »-H «-} «-[*] uj = u2 = %3D (a)…

A: According to our guidelines we can answer only three sub-parts and rest can be reposted.

Q: Check whether the following inner product defined by = x1yı + 2x1Y2 + 2x2Y1 + 5x2Y2, where a = (x1,…

A: Let x,y,z be any vectors and c be any scalar. Then, , is said to be an inner product if the…

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: Only need help on part b.

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Q: 2. a – 2y + z = -6 2x – 3y –- z = 11 -x + 4y – 3z = 28

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Q: O. product there exists positave depnite matrix be a scalav RÉ Prove that a Eymmetric, . let = a…

A: According to the given information, Let < . , . > be a scalar product on R2. It is required to…

Q: (the trace of A). Prove that T is a linear transformation. Let A and B be to matrices in M, and let…

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Q: %3D Show that for all 2, a, BE C, A(a + B) = àa + A8 fiold ofE the

A: (2) We have to show that for all λ,α,β∈C, λα+β=λα+λβ Let λ=a1+ib1, α=a2+ib2, β=a3+ib3…

Q: 2 1 c is a serond dimension complex veetor U and v are elements of c² u= (34 ;, 24 2;), V= (2t;,-2…

A: To find- Euclidean  norm.

Q: atrix L nas the lemen R2 – R1) → R2, R2 + R1 pplied to it to transform it to the matrix

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Q: Find (u, v), ||u||, ||||, and d(u, v) for the given inner product defined on R". u = (-8, 15), v =…

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Q: Let u = (1, –3) and v = (2,5) in R². (a) Find (u, v) and ||v|| with respect to the standard inner…

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