Let a = (– 1, 5, 0) and b = (3,0, – 1). Find the component of b onto a.

Q: Find the coordinate vector of p relative to {p,» P;» P3} for P,. the basis S =

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Q: Find the gradient vector and Hessian matrix for each of the following functions: a) f(x,y) = 3xy² +…

A: As per our guideline we are supposed to answer only one question you can repost other questions in…

Q: Show every vector a in R² can be written as a linear combination of and

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Q: Let B = {1, x, x², x*} be an ordered basis for P3. Find the coordinate vector of f(x) = 4x3 – 72² +…

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Q: (a) a = (2, 6, 0) , b = (4, –1, 1) (b) a =i-j-k, b = }i+j- 4k

A: a) given that  a=<2,6,0> , b=<4,-1,1> a→=2i+6j+0kb→=4i-j+ka→×b→=ijk2604-11…

Q: Suppose v, w e R" and {v, w} is linearly independent. Prove that {v – w, 2v+w} is linearly…

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Q: Let T : R? → R? be defined by T x1 – x2 -2 Let B = U2 = and C = V2 = Find [T, the matrix…

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Q: Write v as a linear combination of u and w, if possible, where u = (1, 2) and w = (1, −1). v = (−1,…

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Q: Show that the set {1, x, x2, ... , xn} is linearly independent in Pn(F).

A: Given, {1, x, x2, ... , xn}

Q: In each part, determine whether the vectors are linearly independent or are linearly dependent in…

A: We have to find the given vectors are linearly independent or dependent  Here year I am solving…

Q: For each matrix A and ordered basis B, find [LA]8. Also, find an invert- ible matrix Q such that…

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Q: Find the matrix A' for T relative to the basis B'. T: R2 > R2, T(x, у) 3 (x — у, 2у - х), в' %3D…

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Q: Let B = (1, x, x², x*) be an ordered basis for P3. Find the coordinate vector of 8x – 6x2 – 9x + 3…

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Q: Let u=(1, 0, -2) and v=(2, -1, 0). Find the components of 3(u-2v).

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Q: ) Let B = {vi =,₂ =, V3 =}. Determine whether B is linearly independent or linearly dependent.

A: Let us consider a set of vectors V=v1,v2,.......vn. The set of vectors are said to be linearly…

Q: Determine if the ODE is a homogeneous DE. If it is, state its degree. 1. у' 2ху2 yx2 +y3 -4/(x³y3)

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Q: Find the matrix A′ for T relative to the basis B′.T: R2→R2, T(x, y) = (2x − y, y − x), B′ = {(1,…

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Q: Find the matrix A' for T relative to the basis B'. T: R2 - R2, T(x, y) = (x – y, y – 4x), B' = {(1,…

A: The given transformation is Tx,y=x-y,y-4x and the basis B'1,-2,0,3.

Q: Find the coordinate vector [x]g of x relative to the given basis B= {b, , b2}. 3 2 b, ,b2 2 -7 - 5

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Q: Find the matrix A' for T relative to the basis B'. T: R2 → R, T(x, y) = (4x – 3y, 5x), B' = {(-2,…

A: We have to find the matrix A' for T relative to the basis B'.

Q: Find a basis fo

A: Given,            A=3-916-26-161-38

Q: Let w = r = Uv, s = u - 3v. Use appropriate forms of the + s²' dw dw chain rule to find and in terms…

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Q: The functions y1, 2, ..., Yn are linearly independent, if and only if W (91, 32, ..., Yn)(to) #0 for…

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Q: Find the coordinate vector of p(x) = 3 - x + 4x2 with respect to the basis B = {1, 1 + x, -1 + x2}…

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Q: Let B, D be the following two bases of R³: -1 B = D= a) Find the change of coordinates matrix Po-s…

A: Solution is below.

Q: Find the coordinate vector ofp(x) = 1 + 2x + 3x2 with respect to the basis B = {l + x,- x, x2} of…

A: Given :           p(x) = 1 + 2x + 3x2            B = 1 + x, - x, x2 of P2

Q: (a) Find the coordinate vector of æ with respect to the ordered basis E = -2 of R3:

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Q: The set B = {1 – t2, t – t², 2 – t + t²} is a basis for P2. Find the coordinate vector of p(t) = 1+…

A: The coordinate vector of p(t) relative to B will be [p(t)]B

Q: ind the matrix A' for T relative to the basis B'. T: R² → R², T(x, y) = (-2x + y, 2x - y), B' = {(1,…

A: Given : T : R2→R2, T(x,y)=(-2x+y,2x-y),B'=1,-1,-1,5 . To find : The matrix A' for T relative to the…

Q: Consider P2(R) with its basis B = (x, x + 1, x² –- 1). Find [x2 + 3x + 5]B.

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Q: Compute the Jacobian of the mapping. G(r, s) = (8rs, 4r + 6s)

A: G(r,s)=(8rs,4r+6s). We need to find the jacobian.

Q: Find a basis for the kernel of the linear operator T(x, y) = (6x - y, -24x + 4y), Using the…

A: It is given that the linear operator Tx,y=6x-y,-24x+4y. Find the kernel of the linear operator.…

Q: Classify and reduce the following equations into canonical form : (a): e"u +e'uy =u. (b): x²u +…

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Q: Find the matrix A′ for T relative to the basis B′.T: R2→R2, T(x, y) = (−3x + y, 3x − y), B′ = {(1,…

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Q: Let Pa represents multiplication by 1+t? with respect to the basis B = {1,t,ť²} for P2 and BU{t,t*}…

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Q: Write v as a linear combination of u and w, if possible, where u = (1, 2) and w = (1, −1). v = (0,…

A: Here u = (1, 2), w = (1, -1) and v = (0, 3) Since v is a linear combination of u and w So consider v…

Q: Suppose v1, ..., Vm is linearly independent in V and w e V. Prove that if vi + w, ..., Vm +w is…

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Q: Find the component of u along v. u = 31 - 24j, v =j

A: component of vecor u along vector v is=u→.v→v→givenu=3i-24jv=j

Q: Find the coordinate vector of p(x) = 5 - 2x + 4x² with respect to the basis B = (1 + x, 1 – X, x?}…

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Q: Find

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Q: Find the matrix A' for T relative to the basis B'. T: R2 - R2, T(x, y) = (x - 3y, 2x), B' = {(-2,…

A: Here we have to find out matrix for the given linear transformation.

Q: Let, T: R²³ R³T (x₂√, z) = (x+√+2, 27¹², 24+32) • Test whether the transformation linear or not T is…

A: Given- T: R3→R3: T x,y,z=x+y+z , 2y+z, 2y+3z (a) To test T is linear transformation (b) To find…

Q: Let T : R² → R³ be the linear map given by [2r1 + 7x2] 2i + 22 Write does the matrix A associated…

A: The given linear map is T:ℝ2→ℝ3Tx1,x2=2x1+7x2, x1-x2, x1+x2 To find the matrix A associated with T…

Q: Let r (t)= - The x component of r' (-1) =

A: r'(t)=<2t,3,5> r'(-1)=<-2,3,5>

Q: Find a and b such that v = au + bw, where u = ⟨1, 2⟩ and w = ⟨1, −1⟩. v = ⟨−6, 0⟩

A: It is given that,  v = au + bw, where u = ⟨1, 2⟩ and w = ⟨1, −1⟩. v = ⟨−6, 0⟩

Q: Show that the set {1, x, x2, ..., xn} is linearly independent in Pn(F).

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Q: Find a and b such that v = au + bw, where where u = (1, 2) and w = (1, –1). v = (0, 12) a =

A: We can find the value of a and b as below.

Q: Suppose T E L(V, W), and w1, ..., wm is a basis of range T.

A: Given that T∈L(V,W)andw1,.......wm is a basis of range T.To prove there exist…