個同 . Find a basis for the Subspace W of R spanned by S What is the dimension of W?

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: Consider the subspace W of R' given by: 900000 W What is the dimension of this subspace? O 1 2 4.

A: In this question we have to find the dimension of this basis.

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: 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: Let Z E R³ | y Prove that Z is a subspace of R³. = Z

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Q: What is the dimensionality of the subspace spanned by V = \v +7w for the following v, w? a) b) d) 12

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Q: Find a basis and the dimension of the given subspace of R4: a + c a – b b+c E R4 -a + b

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Q: 5. Let W be a subspace of a 10-dimensional inner product space V. If dim W = 6, what is dim W¹? (a)…

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Q: Let vị 2,v2 8,and w Determine if w is in the subspace of R generated by v1 and v2.

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Q: Let W = {a + bx + cx? + dx³ € Pg : c = a – b+ 2d} be a subspace of P3. Then a basis for W is:

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Q: Determine whether W is a subspace of V

A: Given

Q: Find a basis for the following subspace of IR°. P = {¤ E R° | x1= x3 = x5, x2 + x4 = 0} What is the…

A: Explanation of the answer is as follows

Q: Find a basis for subspace S of M2,2. s ={ [ ] : 4a – b = 2c + 2d ; a, b, c, d E R - C

A: We have to find basis of subspace S of M2x2 matrix.

Q: 4. Use the definition of a subspace to prove that the set V:= :, y, z E R, y+ : 0 is a subspace of…

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Q: The following subset of R W ((a,b.c): a +b+c 0} is a subspace of R'.

A: Subset of R2 is given W=(a,b,c):a+b+c=0W is subspace if and only if α,β∈W and c∈F(field)⇒cα+β∈Wlet…

Q: R? Which vector stretches the x + y = 0 subspace of ? Why is that? a. (2,1) b. (0,0) c.(1, -1)…

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Q: b) Let W = { 0) * x, y e R}. Show that W is not a subspaces of M2x2. %3D

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Q: S= {[a b c]e R³|b= 3a and c = a +3} is a subspace of R' %3D ylgn O ihi O

A: To check whether S=a b c∈ℝ3|b=3a and c=a+3 is a subspace of ℝ3

Q: 1. Determine whether W ER is a subspace of M. %3D b 2a

A: We have to determine whether W is a subspace of M22.   According top our guidelines we can solve…

Q: Show that the set T= {(a, b, c, d): 2a-3b+Sc-d=0} is a subspace of R'.

A: Given T=abcd∈ℝ4:2a-3b+5c-d=0 Let A be a 1×4 matrix defined by: A=2-35-1 Then the equation…

Q: Determine whether W= [(a, a, b)la, bεR] is a Subspace of R³

A: Given that,  W=a,2,b|a,b∈R

Q: Show that S is a subspace of R2 where S = {x € R²: x=(5k, 10k), k = R}.

A: Given  S = x∈ℝ2 : x=5k, 10k, k∈ℝ. We have to show that S is a subspace of ℝ2.

Q: If S is a subspace of R* and dim(S) = 3, what is the dimension of the orthogonal complement of S?…

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Q: Determine whether W = {(a,2,b)la, b ER} is a subspace of R³.

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Q: Let W = {a + bx + cx? +dx']c = a + b } be a subspace of P3. Then dimension of W is equal to: O 2 O 3…

A: To find the dimension of W.

Q: 5. Let H = {(a - 3b, b-a, a, b): a, b E R}. Show that H is a subspace of R¹.

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Q: What is the dimension of w = {A € M2x2 (R) : A"| =ö} ĄT -2 1 2 This is not a subspace

A: W=AEM2×2(R) : AT1-2=→0  Let A=abcd, a,b,c,dER     AT=acbd     AT1-2=→0  ⇒acbd 1-2 =00 ⇒a-2cb-2d=00…

Q: show what W = {(a,0,b)| a,b E R)  is a subspace of R^3

A: Given : W={(a,0,b)|a,b∈R}   To Show : W is subspace of R3

Q: Which of the following is the dimension of the subspace a W = b :a = b – c and a,b,c,d € R } c Rª ?…

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Q: Determine whether W is a subspace of V = C, where W = {(0, b,c) E C³

A: V=ℂ3 and W=0,b,c∈ℂ3

Q: Consider the subspace W = {(a, b, c) E R³ : a – 26 – 3c = 0} of R³. (a) Is {(5, 1,1)} a linearly…

A: (a) Yes. The detailed explanation is as follows below:

Q: Which of the following is a subspace of p2? O a. R2 x, e R W = Зх, + 1 1. Ob. W = ER| x*2 2 0 C. ER?…

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Q: Which of the following is the dimension of the subspace W = :y = x+z and x, y, z, w e R} CR ? (a) 0…

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Q: Show that W = {(a, 0, b)la, b = R} is a subspace of R³.

A: As per guidelines we are supposed to solve the maximum first questions only .kindly post another…

Q: Find (a) a basis for and (b) the dimension of the subspace W of R4. W = {(s + 4t, t, s, 2s − t): s…

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Q: Consider the subspace W = {(a, b, c) E R³ : a – 26 – 3c = 0} of R³. (b) Is {(5, 1, 1)} a basis for…

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Q: Q7) Find a basis for the subspace and state the dimension. 2с а — b b — Зс la + 2b] Even roll…

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Q: Show that S = {(a,0, b)"|a,b E R} forms a subspace of R³.

A: The solution are next step

Q: Let W = {(a, b, c, d) E R*| a – b = 0,2b + c = d}. i. Show that W is a subspace of R*. ii. Find a…

A: We will prove the following result.

Q: Find a basis and the dimension of the subspace W = {(a+1)x+(2- )x²; a,b e R} of P,

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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: Find (a) a basis for and (b) the dimension of the subspace W of R4. W = {(0, 6t, t, −t): t is a real…

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Q: Let U = a :a ERis a subspace of R? | 2a Is U a subset of R2? Is 0 E U?

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Q: 1. Let V = (Z;)ª, and let W = {(a, 2a, a + 2b, b + c)|a, b, c € Z7} |(a) Show that W is a subspace…

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Q: Let S = { (a, b, c) ER° : b = a +c}. Show that S is a subspace of R'.

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Q: 4. (a) Find a basis for the subspace H of R spanned by the following vectors: 00000 1 (b) What is…

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Q: Find a basis and the dimension of the subspace W = {(a+1)x+(2-b)x²; a,b e R} of P,.

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Q: S= {[a b c]eR* |b = 0} is a subspace of R'. ylgn Ihi O

A: I have proved the basis definition of subspace

Q: Let W be a 3- dimensional subspace of R*, then Dim ( WnW) = Оз O 1 O None of these

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.