W y x+ y+z = 0 is a subspace of R³. Select one: True False II

Q: 3. Show that the set W = {(x, 0) : x e R} is a subspace of R?.

A: In order to show W is a subspace of R2 , we need to prove W is closed under addition. For any two…

Q: rove that W2 = {(a,b) E R² : a = 26²} is not a subspace of R?.

A:

Q: Which of the following is not a subspace of R? Select one: O A. W={X: I1 B W= {X:1= T, of I, = O…

A:

Q: Determine if (x, y, z, t) ∈ R^4 such that y = −x and z = 0, and t = 2x form a subspace of R^4

A: Use the necessary and sufficient condition for a subspace of a vector space

Q: Let W = {a + bx + cx² + dx³[ c – 3d = 0 } be a subspace of P3. Then the dimension of W is equal to O…

A:

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

Q: Let Y = {(x,y,z)| z=-x}. (a) Is Y a subspace of R? Justify. (b) Is Y a vector space? Justify.

A:

Q: The dimension of the subspace W = {A E R™Xn: A is diagonal} is 2. balg j

A: Dimension of the subspace:          If V is spanned by a finite set , then V is said to be finite…

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: 3. State why W = {x = (x1, 2, X3, T4) E R' : a1 + x2 + x3 + a4 < 1} is not a subspace of R. (H.W)

A:

Q: For subspaces V & V*of R° and V±R³, consider the set Š=VUV+. Is 3=R*? (always justify your answer to…

A: No! It's not true that S=R5.See the counter-example below.

Q: For which value of t is the set V below a subspace of R3? V = {(x, y, z) | 5x + 15y = 16x + 3y + 19z…

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Q: Let V = {ax* + bx² + c : a, b, c E R}. Is V a subspace of P4?

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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: {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…

A:

Q: Is the subset V {(x, y, z, w), y = 3z, w = 2x + 1} a subspace of R*? Show the details of %3D your…

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Q: Find the closest point to y in the subspace W spanned by u₁ and ₂. y = 17, U₁ 2, U₂ = 0-16 16 24 31…

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Q: Let X =R, and M = (0} , the M is not subspace of R O True O False

A: Subspace of a vector space

Q: b.) show that IR³ - W₁ + W₂. t C.) Find a subspace V such that IR³ =W₁ U.

A:

Q: Let W = {a + bx + cx² + dx³| c – 3d = 0 } be a subspace of P3. Then the dimension of W is equal to

A: As given W be a subspace of P3.

Q: Verify that V5 is a subspace of RS

A: Please check step 2 for solution.!

Q: Let W = (a + bx + cx? + dx³la + 2c 0 andb-d D 0) be a subspace of P,. %3D Then dimension of W is…

A: Given  W={a+bx+cx2+dx3| a+2c=0 and b-d=0}Since a+2c=0⇒a=-2cand b-d=0⇒b=dwhich gives…

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: Let W = {a + bx + cx2 + dx'|c-3d = 0} be a subspace of P, Then the dimension of W is equal to %3D 4.…

A:

Q: Is T = {(x,y,z)| x+2 y+3z=0} a subspace of R?

A: Subspace

Q: Determine the following is the subspace in R’? W ={(x,y,z):x+y+z=0}

A:

Q: Give a counter example to show that W is not subspace of R³. W=set of (x, y, z) where x + y = 1

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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.

Q: Let W = (a + bx + cx? + dx'la + 2c 0 and b -d 0} be a subspace of P, %3D Then dimension of W is…

A:

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…

A:

Q: Is M = {(x,y,z)|x is nonnegative} a subspace of R³? Yes or No? Justify or give/find a…

A: Given  M =  x, y, z  x is nonnegative

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…

Q: Is W = ((x,y) | xy=0} a subspace of R??

A:

Q: Suppose that X = eR' : 2 + y + z = 0 and r²+y² = z² } . Determine (with justification) whether X is…

A: We have to check whether the set X is a subspace of the vector space ℝ3. We have to give a…

Q: projw(x) is not orthogonal to every vector in the subspace W. O True False

A: We have to check whether the given statement, "projwx is not orthogonal to every vector in the…

Q: Let W = {(" ):a = 2c = b = –3d} be a subspace of M22. Then dimension of W is equal to: None of the…

A:

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: snip

A: We can represent the given set again as: W=xyz:x=3y+1 and z=-2y Let  w1=x1y1z1∈WThen,x1=3y1+1 and…

Q: а о if v = M22 ( R) and W = { : а , bE R } 0 a then .a W is not subspace of .b W is subspace of

A:

Q: Which of the following subsets of R is a subspace? {(:) \ z + y° = 0} {(:) \ +2y = 0} {(;) \ z +2y =…

A:

Q: Which of the following are subspaces of R^3?  W ={(x, y, z) :x+y+z=0} W= {(x,y,z): x2 + y2+ z2…

A: The given vector space is R3. We know that a subset W of a vector space V is a subspace of V if it…

Q: Find the closest point to y in the subspace W spanned by u, and u2. 7 2 y = 21 u1 2 , u2* 3 38 - 1 4…

A: Given that     y = (7,21,38) , u1 = (2,2,-1) and u2 = (-1,3,4) Here we have to find the closest…

Q: (A) Let U1, U2, U3 be subspaces of M2x2(R). If V = U1 e U2 e U3, then dim V = 4.

A: So,  V is the direct sum of the subspaces U1, U2, U3  of M2×2(R) , i.e. dim(U1) = dim(U2) = dim(U3)…

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

A:

Q: If y is not in a subspace W, then y-y is zero. Select one: O True O False

A:

Q: Let W = (a + bx + cx² + dx³[ c – 3d = 0 } be a subspace of Py. Then the dimension of W is equal to

A: Here we will find out dimension of W.

Q: Let W = 2c = b = –3d} be a subspace of M22. a Then dimension of W is equal to: 3 4 None of the…

A: We can solve this as follows: