[5 Find the orthogonal projection ŷ of y = onto the subspace 3 W = Span { uį = 2 u2 3 Ex: 1.23 ŷ =

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.

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Q: Which of the following are subspaces of R^3?  W ={(x, y, z) :x+y+z=0}

A: Given, W=x,y,z:x+y+z=0 Let, 2,-1,1∈W Let, -1∈F

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A: PnF is set of all polynomials of degree nand smaller . PnF denotes the vector space over field F…

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A: To find - Let W = a + bx + cx2 + dx3| c - 3d = 0 be a subspace of P3. Then the dimension of W is…

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: 9. Is Y = {(x,y, z) | y=z} R?? a subspace of

A: ψ={(x,y,z)| y=z}

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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: Find the orthogonal projection ŷ of y: 6 onto the subspace W = Span { ui u2 Ex: 1.23 ||

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Q: 2 -3 Find the orthogonal projection ŷ of the vector y onto the subspace W = Span { u = 1 %3D 8 Ex: 5…

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Q: Suppose U = {(z, 2, ,9) *:1,y € F}. Find a subspace W of F such that F* = U e W.

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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: 2 Find the orthogonal projection ŷ of y = onto the subspace 3 -2 W = Span { ui u2 Ex: 1.23 ŷ =

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Q: (1) Suppose U and W are both five-dimensional subspaces of R°. Prove that UnW + {0}.

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A: Subspace

Q: -3 Find the orthogonal projection ŷ of y = -1 onto the subspace -2 5 W = Span { u1 = -5 u2 = -3 Ex:…

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Q: -4 Find the orthogonal projection ŷ of y onto the subspace 4 W = Span { u1 -5 Uj = u2 Ex: 1.23 : ŷ =…

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Q: 5 1 Find the orthogonal projection ŷ of the vector y onto the subspace W = Span { u = -7 3 Ex: 5 ||

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Q: Let W = (a + bx + cx2 + dx'| c- 3d = 0} be a subspace of P. Then the dimension of W is equal to O…

A: dim(W) = number of vector in the basis of W.

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Q: 3) Explain why S, = {(x, y) E R²:y > 0} and S1 = {(x, x²): x E R} are not subspaces of R?. %3D

A: We will solve both these parts using only basic knowledge of subspaces and vector spaces (in clear…

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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.…

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Q: Find the orthogonal projection ŷ of y = 6 onto the subspace 2 -3 W = Span { ui = 3 Ex: 1.23

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Q: 12. Let K C R" and let V = {x € R" : x ly Vy E K}. Prove that V is a subspace of R".

A: " As per the company guidelines we are supposed to solve first question only. Kindly post the other…

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A: The solution is given in the next step.

Q: 1 1 onto the subspace W = Span -7 Find the orthogonal projection ŷ of the vector y = u = 2 Ex: 5

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Q: 6 H 6 and let W be the set of all x in R³ such that u x = 0. (a) Show that W is a subspace of R³.…

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Q: ) The degree of pa is equal to the dimension of the cyclic subspace Z (a ; T) .

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Q: Let W = {a + bx + cx? + dx*Ia + b = 0 and c – 3d = 0 } be a subspace of P3. Then the dimension of W…

A: Use the concept that dimension of subspace is number of free variables.

Q: W e R"|2, > 0 over the field of reals is a subspace of the specified vector space ER"

A: Given that W=x1x2x3⋮xm∈Rm|x1≥0 and V=x1x2x3⋮xm∈Rm The objective is to show that W is subspace of V.…

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: 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: Is Q = {(x,y,z) | x=2y & z=1} a subspace of R?

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Q: 2 Find the dimension of the subspace H of R spanned by – 12 8 ..... dim H =

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Q: (5) Suppose that T E L(V) is such that all subspaces of V of dimension dim(V) – 1 are T-invariant.…

A: Please check step 2 for the solution.!

Q: What is the dimension of the subspace below? w = sp { J. C a) O 0 b) c)O 2 d) O 3 e) O -1 1,

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