The vector x is in a subspace H with a basis B= {b,,b,}. Find the B-coordinate vector of x. 1 - 4 - 3 b, = b2 -15 - 10 7 4 [x]B =O

Q: A. 2. Find the Basis of the following subspaces of R3: (a) the Plane 5x - 4y+3z 0 (b) the line r= 6t…

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Q: Find the closest point to y in the subspace W spanned by v, and v2. 13 1 5 - 1 y = 1 1 , V2 = 1 - 1…

A: Given y=13-112,v1=11-1-2,v2=5103. The orthogonal projection of y onto span of v1, v2 is…

Q: Which of the following is a subspace of R? O A. All vectors of the form (a, 0,0). O B. All vectors…

A: Subspace of a vector space:  A subset V of ℝn is said to be a subspace of ℝn if 1. The zero vector…

Q: (a) give a geometric description of, (b) find a basis for, and (c) find the dimension of the…

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Q: Q: Let W, ={(a, B.Y, 8): a=y+28, y= 28} and W2 {(a, B.Y, 8):a-y-0} be two subspaces of V,(R). Find a…

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Q: 1. Let V = (Z7)4, and let W = {(a, 2a, a + 2b, b + c)|a, b, c E Z7} |(a) Show that W is a subspace…

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

A: According to the given information, X is a vector in a subspace H with basis B. it is required to…

Q: 5 3 Find a basis of the subspace of R* consisting of all vectors perpendicular to v. -6 Let i 7…

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Q: For the given subspace, H, (i) find a basis for the subspace, and (ii) state the dimension. 2c (а) Н…

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Q: 3.) Find (a) basis for and (b) the dimension of the subspace W = {(s + 4t, t,s, 2s - t):s and t are…

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Q: 14. The vector x is in a subspace H with a basis B = {b₁,b₂}. Find the B-coordinate vector of x. (a)…

A: We can solve this as follows:

Q: Given v = find the coordinates for v in the subspace W spanned by -7 u1 = and uz -1 -28 Note that uj…

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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. %3D 1…

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Q: Which of the following statements is TRUE? a) { [a 2 36] ; a, be R} is a subspace of R. b) {t – 1,3t…

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Q: 1. Let V = (Z7)4, and let W = {(a, 2a, a + 2b, b + c)|a, b, c E Z7} (a) Show that W is a subspace of…

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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 an orthogonal basis of the subspace of spanned by the vectors 日目 4 (a) (b) (c) (d) 30 e.None of…

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Q: The sequence B = (|1 3)) is a basis for the subspace U = {{ r2| |r1 – 3r2 + 2r3 = 0}. 13 The vector…

A: We have to find the coefficient for linear combination

Q: Find an orthogonal basis of the subspace of spanned by the vectors 3. (a) (b) (c) (d) O a O c O b O…

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Q: 1. Let v, = (43 2 1), v, = (-2 0 -1 0), v3 = (0 3 0 1) a) Find the subspace of R* spanned by these…

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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: Which of the following is a subspace of R? O A. All vectors of the form (a, 0, 0). B. All vectors of…

A: To choose correct option we will use the following theorem Theorem: A non-empty subset W of a vector…

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: The vector x is in a subspace H with a basis ß= (b₁, b2]. Find the B-coordinate vector of x. -6-0-3…

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Q: Let v, = (43 2 1), v2 = (-2 0 -1 0), V3 = (0 3 0 1) a) Find the subspace of R" spanned by these…

A: The given vectors are: v1=4, 3, 2, 1, v2=-2, 0, -1, 0 and v3=0, 3, 0, 1 The subspace W spanned by…

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: (000 x2 {x = |x1 – x2+ x3 - a4 = 0}, B x3 11. Let V x4 In 12-14 find the

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Q: Consider the vectors R³, and let W be the subspace span{1, 2}. a) Find an orthogonal basis for W. 3…

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Q: In each part, find a basis for the given subspace of R', and state its dimension. a) All vectors of…

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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: 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: 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: In each part, find a basis for the given subspace of R, and state its dimension. a) All vectors of…

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Q: which of the following is subspace of the vector space V = R³ A) All vectors of the form (1, 1, c).…

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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: The vector x is in a subspace H with a basis B = {b, b2}. Find the B-coordinate vector of x. - 3 2 2…

A: Coordinate of a vector

Q: Lct Vị and V2 be subspaces of R" such that Vị C V2. Show that any vector v E R" can be uniquely…

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Q: Consider the vector space of real 3 x 3 matrices M3,3. i: Consider S {A € M3,3|A = A"} Show that S…

A: Since you have asked multiple questions, we will solve first one for you. If you want other question…

Q: 6. (a) Find a basis for the subspace of R' spanned by 1 4 7 -5 7 4 w = 4 -5 (b) Using part (a),…

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Q: It can be shown (but you need not do so) that b 0 с d :]|++d} W = a +c= a subspace of M2.3. Find a…

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Q: In each part, find a basis for the given subspace of R4 (1) All vectors of the form (a, b, 0, 0).(2)…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

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

A: Solution:Given b1 = 4-11 , b2 = -14 , x = 8-17let u,v be scalaris such that,x = ub1 + vb2⇒ 8-17 =…

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

A: Let V be a vector space over field F . Let W be a subset of V then W is said to be subspace of V…

Q: Find an orthogonal basis of the subspace of spanned by the vectors 目 目 [2] (a) (b) 3 (c) (d) 12 2 3…

A: We have to find an orthogonal basis of the subspace.

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.