Q: -4 Find the orthogonal projection ŷ of y = 4 onto the subspace 3 -3 W = Span { uj U2 = 2 Ex: 1.23
A: With the help of definition of projection of a vector on a subspace, we solve this problem.
Q: Let W - (a + bx + cx + dx'l a +b-0 and c - 3d = 0) be a subspace of Py. Then the dimension of W is…
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Q: Find the closest point to y in the subspace W spanned by v, and v2. 13 1 5 - 1 y = 1 1 , V2 = 1 - 1…
A: Given y=13-112,v1=11-1-2,v2=5103. The orthogonal projection of y onto span of v1, v2 is…
Q: Let W = {a + bx + cx² + dx³[ c – 3d = 0 } be a subspace of P3. Then the dimension of W is equal to O…
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Q: 2. Find the closest point to y in the subspace W spanned by vị and v2. 3 1 -2 y V2 13 3
A: To find The closest point y in the subspace W spanned by v1 and v2.
Q: Let W = {a + bx + cx² + dx³| a + b = 0,c – a = 0, and d – 3a = 0 } be a subspace of P3. Then the…
A: dimW = 1
Q: Let A = { | 2.x |x € R}. Is A a subspace of R³? З Let B x + y + z = 0}. Is B a subspace of R³?
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Q: Let S = E M2x2; a = d and b +c = 0} be a subspace of M2x2- Then the dimension of S is equal to: 1 4
A: S=abcd∈M2×2; a=d and b+c=0 be a subspace of M2×2
Q: If V is the vector space of real valued continuous functions , then show that the set W of all d’y…
A: Our Aim is to show that the set W of all solutions of the differential equation3d2ydx2-5dydx+7y=0…
Q: Let W = {a + bx + cx² + dx°|c - 3d = 0} be a subspace of Pa. Then the dimension of W is equal to 3.…
A: PnF is set of all polynomials of degree nand smaller . PnF denotes the vector space over field F…
Q: -2 Find the orthogonal projection ŷ of y = 3 onto the subspace 2 -2 W = Span { u , U2 Ex: 1.23 : ||
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Q: 10. Is 2 = {(x, y,z)| x=2 y & z=1} a subspace of R³?
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Q: True or False: If U and W are subspaces of a finite dimensional vector space and UnW = {0}, then U°…
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Q: 9. Is Y = {(x,y, z) | y=z} R?? a subspace of
A: ψ={(x,y,z)| y=z}
Q: 10. Let Y = {(x,y,z)| z=-x}. (a) Is Y a subspace of R³? Justify. (b) Is Y a vector space? Justify.
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Q: Find the orthogonal projection ŷ of y = onto the subspace W = Span { uị u2 5 Ex: 1.23 : ŷ =
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Q: Determine is Question 2 whether W = W = {(a; z { (a; 2; 6) | α; 6ER} subspace of R
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Q: Find the closest point to y in the subspace W spanned by u, and uz. 17 1 2 %3D u1 = 0 |, u2 = - 1 2…
A: To find The closest point to y in the subspace w spanned by u1 and u2
Q: 1 -1 Find the distance from y to the subspace spanned by u. U= y= NO N1
A: Here given vectors are: u=2021y=1-11-1
Q: {l: ol E M2x3: a = b = c = -3d } be a subspace of M2x3- Let W = d Then dimension of W is Оз 1 О4 O 2…
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Q: Find the orthogonal projection of the vector v onto the subspace S. v = |2 S =
A: projS(V) = (u1.v/u1.u1)u1 + (u2.v/u2.u2)u2
Q: Q.4 Show that U {(x, -x) |x in R} is a subspace of R. %3D
A: To Prove U is a subspace of vector space V 1) 0∈U If x, y∈U and a∈V 2) Closed under vector…
Q: What is the dimension of the subspace W = {A = [aij] € R4x5|a45 = 0} dimW = Ex: 5
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Q: b.) show that IR³ - W₁ + W₂. t C.) Find a subspace V such that IR³ =W₁ U.
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Q: Let W = (a + bx+ cx + dx'|a+ b= 0 and c -3d = 0 ) be a subspace of P Then the dimension of W is…
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Q: Find the distance from the vector -1 y = -5 10 to the subspace W spanned by -2 1 u 0 and v= 2 ||
A: The given vector is y=-1-510 and the subspace is u=-200, v=12-1.
Q: Suppose U and W are two-dimensional subspaces of R3. Show that U∩W≠{0}
A: We want to show that U∩W≠{0}
Q: 1 for which x value span the vector subspace? -1 13 - 2 -1 O A) 2 в) .1 O C) 0 D) 1 O E) -2
A: We have to find x
Q: Is T = {(x,y,z)| x+2 y+3z=0} a subspace of R?
A: Subspace
Q: -4 Find the orthogonal projection ŷ of y onto the subspace 4 W = Span { u1 -5 Uj = u2 Ex: 1.23 : ŷ =…
A: Given
Q: Suppose that U cr|xyer F4 y EF, U is a subspace of F4- you don't have to! Find a subspace V of F4…
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Q: and T are subspaces of V, then SUT
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Q: Is W = ((x,y) | xy=0} a subspace of R??
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Q: Q.4 Show that U {(x, -x) |x in R} is a subspace of R?. %3D
A: Consider the given set. U=x,-x|xinR Let, consider that, f,g∈V And f, and g is defined as.…
Q: What is the value of a if the solution set of the equation x y z 1 1 2 3 1 det 2 3 4 1 O is a…
A: Given solution of the equation…
Q: 4) Find all values of h such that Y will be in the subspace of 3. R spanned by VI) V2, V3 if V I V2…
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Q: Consider the set S = y ER : 3x – 5y = 0, x + z =- . Is this a subspace of R ? Explain why or why…
A: Given set is S=xyz∈R3:3x−5y=0, x+z=4. We have to check whether the set S is the subspace of R3 or…
Q: . Let W₁ -00--00 and W₂ = (b) 1 equal to (a) 0 be subspaces of R³. Then dim(W₁ W₂) is (c) 2 (d) 3
A: We have to solve given problems:
Q: Let S = {[" e Mzxzi a = d and b + c = 0} be a subspace of M2x2- Then the dimension of S is equal to:…
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Q: Let S = {" E M2xzi a = d and b+c 0 be a subspace of M2x2. %3D Then the dimension of S is equal to: 4…
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Q: 2 2 , find the closest point to v in the subspace W spanned by 6 and 3 Given i = 6. 1 12
A: To find The closest point to V in the subspace spaneed by the given vectors.
Q: In R, let S be the set of all vectors with third component 0. { a S = ER Show that S is a subspace…
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Q: Let W {a + bx + cx2 + dx³| a+b = 0 and c- 3d = 0} be a subspace of P3. %3D Then the dimension of W…
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Q: 2. The subspace (a) 2y x+y+z=0 1 in R3 is a plane whose equation is x-2=0 (b) y (c). x-2y+z=0 Py27.…
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Q: and uz = Find the closest point to y = in the subspace W spanned by u1 = The closest point is
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Q: Find the orthogonal projection ŷ of y = -5 onto the subspace 6. -2 W = Span { uį 4 3 u2 %3D -2 Ex:…
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Q: Let S= +c = 0 be a subspace of Mzxa- Then the dimension of S is equal to: 2.
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Q: Show that the solution set to a system of equations of the form au*, + Azyš, + + a, x = 0 Inn + ar =…
A: The given system of homogeneous linear equations is equivalent to a matrix equation of the form: Ax…
Q: Find the closest point to y in the subspace W spanned by v1 and v2 2 1 y = -2 -3] 1 2 а) b) 2 c) 1…
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Q: 49. Let A be a fixed n x n matrix and let S = {B e Mnxn | AB = BA} %3D Is S a subspace? Explain.
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Could you tell me whether (A) is True or False with explanations?
Thank you.
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- Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}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.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 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 the bases for the four fundamental subspaces of the matrix. A=[010030101].Give an example showing that the union of two subspaces of a vector space V is not necessarily a subspace of V.
- In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. 34. ,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?In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V=3, W={[a0a]}