[x-y+z] y-z 2x + y GOO 5.2. Determine ker(T) and use the result to determine whether T is singular or nonsingular Consider the linear mapping T: R³ R³ defined by T fer 5.1. Find the matrix A of Trelative to the basis B = S -3+6₂ 9x2x

Q: 0. -6 2. be an orthogonal basis for the vector space R°with the Euclidean inner product (i.e. dot…

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Q: Consider vị =[1 v2 = | 1) and v3 = ( 0 ) as vectors in R³. Let T: R3→R³ be a linear operator such…

A: We have to find out solutions

Q: Let V be the plane with equation ₁ + 3x2 − 4x3 = 0 in R³. Find the matrix A of the orthogonal -14]…

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Q: For a vector b = (-2, 1, –2) and a plane P : 3r – 2y – 4z = 0 (a) Compute a basis of P. (b) Compute…

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Q: Dases C= and E on R3, (i) Find the vector v3 of R' whose component vector with respect to C is [v3]c…

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Q: 2. Define two ordered bases B = and E = on R³. (i) Find the vector vị of R³ whose component vector…

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Q: Let V be the vector space of functions spanned by B = {bị = 6 sin æ + 4 cos a, b2 = 2 sin æ + 7 cos…

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Q: Consider the basis D = {(1, 1, -1), (2, 1, 3), (-1, 2, 1)} of R3 and the vector v = (1, 1, 1) in R3.…

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Q: 2. Let B₁ be the basis 2²e², re², e² of V = span(2²e², zeª, z), and B₂ be the basis of that the map…

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Q: Let V be the plane with equation 2₁ +222 + 3x3=0 in R³. Find the matrix A of the orthogonal…

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Q: Let V = P² be the vector space of polynomials of degree at most 2, and let B be the basis {f1, f2,…

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Q: Consider the ordered basis B = {(1,-1,0), (1, 1, 1), (0, 1, 1)} of R³. the coordinate vector v =…

A: Consider the ordered basis B=1,-1,0, 1,1,1, 0,1,1 of ℝ3.   To Give: The coordinate vector v=-2,-1,0…

Q: Let W be the plane with the equation 3x − y + 6z = 0. Find the standard matrix P for the orthogonal…

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Q: -8 Let V be the plane with equation ₁ + 3x₂ + 2x3 = 0 in R³. Find the matrix A of the orthogonal…

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Q: Let B = {bj, b2} and C = {c],c2} be bases for a vector space V, and suppose bj 3 бс1 — 2с, and bz —…

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Q: Let V be the plane with equation 1 + 4x2 + 5x3 = 0 in R³. Find the matrix A of the orthogonal…

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Q: Find a basis B for the T domain such that the T matrix relative to B is diagonal. T: R^3 → R^3: T(x,…

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Q: Let the basis vectors be given by a = [3,1] and 6 = [3,3]. Give the image of a general coordinate…

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Q: 2. Let ū = (-1, 2, 1), ở = (1, – 1,–1) and w = (2, 3, 0). Find the coordinates of (2,4,4) with…

A: Using gauss Jordan elimination method to find the value.

Q: Find the dimension and a basis of U = r2s+t 0 -3r s-t r, s, tER

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Q: find the orthogonal complement W' of W  and give a basis for W' of the following:  W = {[x y z]:…

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Q: Let 1 2 3 A = x y z 2 3 4 where x = (x, y, z) = R³. Find a basis of W = {x = (x, y, z) = R³ : det…

A: To find a basis for W, we need to determine the values of x that make det(A)=0. The determinant of A…

Q: 3) Let T d b }]= la + 1b + 1c + 5d + 2e +2f la + 2b + 0c + 5d + 3e + 1f 3a + 4b +3c + 17d+ 8e +6f…

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Q: Consider the basis 5 = {v1, V2, V3} for R°, where v: = (1, 1, 1), v2 = (1, 1, 0), and va = (1,0,0),…

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Q: Prove that if A has n as a minimum then B = {x ∈ R | ∃a ∈ A, x = −3a} has −3n as a maximum

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Q: Find the coordinate vector for w relative to the basis S= {u1, u2} for R2. uj = (1, 0), u2= (0, 1);…

A: Here we use basic defnition of change of basis coordinate

Q: Let B = {b₁,b2, b3} be a basis of R³ where -0-8-0 b₂ = -4 b3 -3 b₁ = 2 5 Let V= - 5 Find the vector…

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Q: 6. Let V = span{1+x²,x}. Two ordered bases for V are Si = {1+a², x} and S2 = {1+x + x², 2+ x + 2a²}.…

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Q: Let P2(R) be the vector space of polynomials over R up to degree 2. Consider {1+x – 2x?, –1 +x+x², 1…

A: Consider the provided question, Given that,  B=1+x-2x2, -1+x+x2, 1-x+x2B'=1-3x+x2, 1-3x-2x2,…

Q: 8B The linear representation is given f:R³ R³: (x,y,z) →f(x, y, z)=(x+2y+z, -2x+2z, 4x-4y+4=) Find a…

A: The given function is, f(x,y,z)=x+2y+z, -2x+2z, 4x-4y+4z. To Find: A rectangular matrix C whose…

Q: F(x,y, z) = 5x² + 2y² + 4xy + xz

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Q: 4. Consider the subspace W 3x-2y -2x + y: x, y eR of R³. x+y (a) Find a basis for W. (b) Find a…

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Q: Let V be the plane with equation ₁ + 3x2 + 4x3 = 0 in R³. Find the matrix A of the orthogonal…

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Q: Consider two bases B = {b1,b2} andC : such that bị = cq – 4c2 and b2 = 6c1 – 5c2. Find the…

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Q: 2. Let B₁ be the basis r²e, ze, e of V = span(r²e², xe, x), and B₂ be the basis is H.6 of w that the…

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