Determine is Question 2 whether W = W = {(a; z { (a; 2; 6) | α; 6ER} subspace of R

Q: Determine whether W = {a + 2x + bx²|a, b = R} is a subspace of P2.

A: Explanation of the answer is as follows

Q: Determine if the set W of vectors (x1 , x2) in R such that xr? + x2 = 1 is a subspace of R’.

A: W is not a subspace of R²

Q: 3. Determine whether X1 W E R? : x² + x2 = | X2 is a subspace of R².

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Q: If v1 and v2 are in R" and H=Gen{v1, v2}, then H is a subspace of R" Justify

A: Given that : and are in  Let Now, we  have to recall  the definition of subspace of a…

Q: (1) Consider the space M2×2 (R) of 2 x 2 matrices equipped with the usual addition and scalar…

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Q: Determine whether H is a subspace of M22. Give reasons! -X IX H={A€ M22 : A = 0 2x

A: Set of all 2*2 matrices denoted by M22 forms a vector space. We have to determine whether H is a…

Q: 4: Let H1 and H2 be two subspaces of R". Show that H1 n H2 is also a subspace of R".

A: To show a set W to be a subspace of the of a space X if a,b∈W then a+b∈W   and for a scaler λ and…

Q: 2. Determine whether W = {a + br + cr?; a, b, c € R, a · b.c= 0} is a subspace of P2.

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Q: Determine if the set W of vectors (X1 , X2) in R such that x1² + x2 = 0 is a subspace of R?.

A: We have to determine whether W is a subspace of R^2 or not.

Q: Q3 shew that W2 = subspace of R2 is a

A: To show any subset of vector space is a subspace , prove the following condition : Set is closed…

Q: 1. Determine whether w - {[:]•r:a-4-0} X1 E R? : : x1 – 23 = X2 is a subspace of R?.

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Q: 5а+ 2b Decide whether the set of all vectors of the form is a subspace of R³ or a

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Q: What is the dimension of the following subspace U of R2x2 ? 3 U = span({ }) -2 -2

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Q: 19. Prove that the set of all vectors in R³that satisfy the equation x₁ = 3x2, is a subspace.

A: (.)  Let set  'S'  is given by ,        S=x1,x2,x3∈ℝ3  :  x1=3x2 or   S= x1,x2,x3∈ℝ3 :  x1-3x2=0…

Q: If W is a subspace, then ||projwv||² + ||v – projwv||2 = ||v|?.

A: Given W is a subspace of a vector space V. Now projWv denotes the projection of vector v onto the…

Q: Determine whether or not W = {[a, a?, b] | a and b are real numbers} is a subspace of R³. Justify…

A: See the detailed solution below.

Q: 3. Determine whether the set W = {(0,x2, 3, x4) : where x2 and x4 are real numbers} is a subspace of…

A: Subspace of a vector space

Q: Which of the following sets are subspaces of R³: W1 = {(x1, x2, X3) : x3 = 2x1 – 4x2}; W2 = {(x1,X2,…

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Q: Select one: a. S={ X2 %3D b. , X €R} S={ 1 C. X 1 X1=2x2} X2 O d. S={ X1=X2}

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Q: The set of all vectors in R squared  that satisfy 3x+4y=1 is a subspace of R squared . True False

A: 1. The set of all vectors in R squared that satisfy  3x+4y=1  is not a subspace of R squared.  i.e.…

Q: Q4. Check the following set is a subspace of R3 or not U = ((x1, x2,x3)| x, = v2 x} %3D

A: The given subset of ℝ3 is: U=x1, x2, x3 |x2=2x1 Definition: Let W be a subset of the vector space V.…

Q: Show that every subspace of ℝ is either {0} or ℝ.

A: Given: ℝ. To Show: Every subspace of ℝ is either {0} or ℝ.

Q: Solve the following questions: Q1) Check whether the set W = {(2a + 5b, –a + b, 3a + 4b); a, b are…

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Q: [{-----} x+y+z=-7 A. B. Which of the following sets are subspaces of R³ ? C. D. Z X Z +2=0} 7x -5x…

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Q: H.W/ let S= [[3] ; X70, ує a subset of R². IS of 1R² be Subspace J-Jubour

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Q: One of the following subsets of R is not subspace. Select one: a. S={ XER) b. S= X2 S= S= X2.

A: Four sets are given. They are subsets of R2 , we need to find the set which is not a subspace of R2.

Q: Find all values of h such that y will be in the subspace of R³ spanned 3] by v1, V2, V3 if v1 =| 2|,…

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Q: Subspace of IR" is 3, True faulse I or

A: Here given set V=xyz∈ℝ3: x-2=y+1=z

Q: Is this a subspace of M

A: Introduction: A vector space that is totally contained within another vector space is known as a…

Q: V = a C |a+b+c= 2, 3a - c = 1, a-b+c=3

A: We know that any subspace of a vector space should contain the zero vector of the vector space.

Q: Let U 2xy = 1. Note that geometrically, U is a linear. Is U a

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