Find the dimension of the subspace U = {[x, y, z, t]|x+4y-z = 0; x-2z+ t= 0}. Select one: а. 4 b. 2 с. 1 d. 3
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![Find the dimension of the subspace U= {[x, y, z, t] | x+4y-z = 0; x-2z+ t= 0}.
Select one:
а. 4
b. 2
с. 1
d. 3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd44c5b45-5071-4ae3-b102-09ebadced1ce%2Faa8aa397-f7c5-4aa3-b116-c870fccc0fd6%2F3cftq3a_processed.jpeg&w=3840&q=75)
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- Repeat Exercise 41 for B={(1,2,2),(1,0,0)} and x=(3,4,4). Let B={(0,2,2),(1,0,2)} be a basis for a subspace of R3, and consider x=(1,4,2), a vector in the subspace. a Write x as a linear combination of the vectors in B.That is, find the coordinates of x relative to B. b Apply the Gram-Schmidt orthonormalization process to transform B into an orthonormal set B. c Write x as a linear combination of the vectors in B.That is, find the coordinates of x relative to B.Let V be an two dimensional subspace of R4 spanned by (0,1,0,1) and (0,2,0,0). Write the vector u=(1,1,1,1) in the form u=v+w, where v is in V and w is orthogonal to every vector in V.Let B={(0,2,2),(1,0,2)} be a basis for a subspace of R3, and consider x=(1,4,2), a vector in the subspace. a Write x as a linear combination of the vectors in B.That is, find the coordinates of x relative to B. b Apply the Gram-Schmidt orthonormalization process to transform B into an orthonormal set B. c Write x as a linear combination of the vectors in B.That is, find the coordinates of x relative to B.
- Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}Let A be an mn matrix where mn whose rank is r. a What is the largest value r can be? b How many vectors are in a basis for the row space of A? c How many vectors are in a basis for the column space of A? d Which vector space Rk has the row space as a subspace? e Which vector space Rk has the column space as a subspace?Find the projection of the vector v = [1 0 −2]T onto the subspace
- if v is in R3, does the set of vectors x with v x x=0 is a subspace?Let V = { [x y z] in ℝ^3 ∶ z = 2x - y }. Is V a subspace of ℝ^3? If it is, what is the dimension of V? Any help (especially with details) would be greatly appreciated.What is the dimension of the sum of subspaces V and W in R3[x], where V={f∈R3[x]∣ f(0)=0} and W=span{x}? (a) 0.(b) 1.(c) 2.(d) 3.(e) 4.
- Determine if (x, y, z, t) ∈ R^4 such that y = −x and z = 0, and t = 2x form a subspace of R^4Find the orthogonal projection of the vector [ 49 49 49] onto the subspaces of R3 spanned by [2 3 6], and [3 -6 2].Let V = R3 and W ={(a, b, c) ∈ V | a + b = c}. Is W a subspaceof V? If so, what is its dimension?
