Find the dimension of the subspace spanned by the given vectors. - 2 11 8 1 4 - 3 3 - 5 - 29 21

Q: Which of the following is the dimension of the subspace b W = :a = b - c and a, b, c,d eRC R* ? (a)…

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Q: Determine the dimensions of the following subspaces of R* a) All vectors of the form (a, b, c, d),…

A: We have to find the dimensions of vector

Q: The sets B={[1 2 2 1]T;  [1 0 2 0]T;  [2 0 4 -3]T} and B'={[0 2 0 1]T;  [2 1 4 -1]T;  [1 2 2n 4]T}…

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Q: The vector x is in a subspace H with a basis B = (b, ,b2). Find the B-coordinate vector of x. - 1 ,…

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Q: 14 a Fet W be the subspace consisting of all vectors of the form 12 a -14 b where a andb are real…

A: Given W is the subspace consisting of all vectors of the form 14a12a-14bb, where a and b are real…

Q: Find an orthogonal basis of the subspace of spanned by the vectors E) - 6A- EQ) (a) (b) (c) (d) 80…

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Q: Q;:Is W={A€ M3(R): a11+a22+a33=1} a subspace of M3(R)?.

A: Note :- A subset S of a vector space is said to be subspace iff  1.S is closed under vector addition…

Q: 2 3 Let vi V2 V3 2 and w = 3 2 a. Is w in {v1, V2, V3}? How many vectors are in {v1, v2, V3}? b. How…

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Q: -2 3 Find the vector in the subspace W spanned by which is 1 27 closest to L 20] Answer:

A: *As this problem is related to Projection matrix, hope you know how to find inverse of a matrix,…

Q: Find the closest point to y in the subspace W spanned by V1 and v2 4 y = V1= V2 = 2 -2 1 a. b. d.

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Q: -9 4 -3 -21 Find the vector in the subspace W spanned by which is closest to –1 -3 -5 Answer:

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Q: -8 a) Is the set of all vectors x = u + tv, wheret ranges over all real numbers, a subspace of R3 ?…

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Q: Find the dimension of the subspace U={[a+c, b+c, a+2c+b] | a, b, c in R} Select one: a. 2 b. 4 c. 1…

A: We have given a subspace ,  U = a + c , b + c , a + 2c + b / a , b , c ∈ ℝ We need to find dimension…

Q: Let ?1 = (4 3 2 1), ?2 = (−2 0 -1 0), ?3 = (0 3 0 1) a) Find the subspace of R^4 spanned by these…

A: Note: There are many long answer for subparts in the questions. So I will answer the first two…

Q: Which of the following sets is NOT subspace of IR? 2 Span -5 {8} Г1 2 31 The set of solutions to the…

A: solve the following

Q: The vector x is in a subspace H with a basis B = {b, ,b2}. Find the B-coordinate vector of x. %3D 1…

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Q: Find the closest point to y in the subspace W spanned by v, and v2. 11 9- -1 3. The closest point to…

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Q: Find the closest point to y in the subspace W spanned by v₁ and v₂. y= 9 15 4 9 The closest point to…

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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: Qi:Is W={A€ M3(R): a1+a22+a33=1} a subspace of M3(R)?.

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Q: Find the dimension of the subspace spanned by the given vectors. - 1 - 7 4 3 2 - 1 - 10 7 ... The…

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Q: Which of the following sets is NOT a subspace of R'? {E} [1 Го 2 31 The set of solutions to the…

A: Following sets are given

Q: 4 6' Let S be the subspace of R° spanned by the vectors and and let b = 3 Find the point in 4 S that…

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Q: 3 5 2 and find the closest point to i in the subspace W spanned by -5 Given i -6 3

A: Givenv→=34-55and let s1→=52-61 and s2→=0734The formula of orthogonal projection of v onto span of s1…

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: The vector x is in a subspace H with a basis B= {b,,b,}. Find the B-coordinate vector of x. 1 - 4 -…

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Q: Which of the following are vector subspaces of of IR³? a) all vectors of the form (a, b, c), where b…

A: a) all vectors of the form (a,b,c), where b=a+cb) all vectors of the form (a,b,c), where b=a+c+1

Q: За+b The set of all vectors H: 3b +a : a, b real numbers is a subspace of R3. %3D 3a+3b +1] True…

A: Since a subspace contain zero vector so we check first whether the zero vector is in the set H or…

Q: Given v find the closest point to v in the subspace W spanned by 3 and |3D -2 3 221

A: Here, v⇀=453-7v1=3221v2=-26-2-2

Q: 7. The vector i = is in a subspace II with hasis B- 32 Find the B-coordinate vector of

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Q: For the subspace a H= b :a-5b+4c=0 d a basis is 1 O True O False

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Q: Find the dimension of the subspace spanned by the given vectors. 2 5 4 9 24 - 19 The dimension of…

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Q: 16 2. Consider the vectors: u= -2 ,V = 0 ] and w= 4 4 -8 a) Is the set of all vectors x = u + tv,…

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Q: The vector x is in a subspace H with a basis B = {b, ,b,}. Find the B-coordinate vector of x. 1 - 2…

A: Given that, b1=14-2; b2=-2-73; x=15-3 Since B = b1, b2 is the basis, xB is the linear combination of…

Q: 7. Let V be a 70-dimensional vector space and let W₁ and W2 be 30-dimensional subspaces. What is the…

A: Given V be an 70-dimensional vector space  W1and W2be 30-dimensional subspaces A vector space is a…

Q: -5 6 Given v -8 ind the coordinates for v in the subspace W spanned by -7 -4 2 3 -2 1 Uz 5 Uz -1 and…

A: Step:-1 Given that  v=-5614-8 and u1=021-11,   u2=-735165,  u3=00-101  and  u4=-4-21-21 And u1, u2,…

Q: Find the closest point to y in the subspace W spanned by u₁ and ₂. 13 y = 19, U₁ = 28 O 26 20 0-2…

A: Given y=131928, u1=22-1,  u2=-134   To Find: The closest vector to y in the subspace W spanned by u1…

Q: Find bases for the four fundamental subspaces of the matrix A. 1 4 9 A = 0 8 0

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Q: 2. (a) Write one of the four vectors 3. 8. as a linear combination of some or all of the others. (b)…

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Q: The vector x is in a subspace H with a basis B = {b1, b2}. Find the B-coordinate vector of x. b1 b2…

A: The given basis is - β=[b1,b2]b1=2-24 ,b2=61-3 , X=410-22 To find β-coordinate vector of x.

Q: Consider the vectors: V1 = (2,0,0,-2), |V2 = (–14 –7,–12,54). V3 = (0,1 1|-6) V4 =…

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Q: a 6. Let H be a subspace of M2x2 whose vectors are of the form Then, B 2 is a basis for H. 7 Find…

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Q: (a) Write one of the four vectors -3 3 2 8 as a linear combination of some or all of the others. (b)…

A: Given: u→=-312, v→=-125, w→=138 and x→=-7-1-4 To find: a) One vector is linear combination of some…

Q: The vector x is in a subspace H with a basis B = {b, ,b,}. Find the B-coordinate vector of x. 2 b1…

A: We have given the basis   B=b1,b2where b1=21 , b2=-13   and we have a vector x = 49in a subspace H…

Q: Find the closest point to y in the subspace W spanned by v, and v2. 1 - 2 - 1 1 2 y = V1 = 1 %3D V2…

A: The closest point to y in W is the projection of y on W.

Q: 3. (a) Write one of the four vectors ü =| 1 2 3, = as a linear combination of some or all of the…

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Q: Find the closest point to y in the subspace W spanned by v, and v2. 3 1 - 1 - 4 - 1 y = 1 1 ,V2 - 1…

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Q: 1) LetF1 be the subspace generated by the vectors (0, 1, 1), (0, 0.1) and 2 the subspace generated…

A: In this question, concept of subspace is used. Subspace A subspace is a vector space that is…

Q: The vector x is in a subspace H with a basis B = {b, ,b2}. Find the B-coordinate vector of x. - 1 8…

A: Let β={ u1  ,u2  , ......., un } be an ordered basis for a finite dimensional vector space V then…

Q: Let W be the subspace of R spanned by the vectors 3 and -6 12 Find the matrix A of the orthogonal…

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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.