ind the closest point in the subspace with the (not orthogonal) basis {b1, b2, b3} to the head of the ector u. -1 b3 : 3 = %3D

Q: Find a basis for the subspace of P3 consisting of all vec- tors of the form at 3 + bt 2 + ct + d,…

A: Given: The vectors are of the form: at3+bt2+ct+d Also given that: c=a-2db=5a+3d Putting the given…

Q: Show that W is a subspace of R¹.

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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: Let X = 1 ,and let V = {A E M2(R) | AX = XA}, a subspace of M2(R). 0. Find a basis for V, and write…

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Q: 4.) Determine the dimension of thr subspace of M21 consisting of vectors of the form [a – 2b] a + b…

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Q: The set W of all 2x3 matrices of the form a I where c = a + b, is a la 0 subspace of M23. a. Find a…

A: on solving this we will get

Q: Let S = {i, j} is a basis of R² and let W = {(x, y), x + y = 0} a- Show that W is subspace of R², b-…

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Q: Use the inner product represented by = u¡V¡ +2 uv; + uzV3 in the following questions, where u- (1,…

A: Given: The inner product  <u, v> =u1v1+2u2v2+u3v3, u=(1, -2, 2) and v=(0, -2, 3) are the…

Q: Find an orthogonal basis of the subspace of spanned by the vectors 目目 。啡3, 。翻 3 -9 (а) (b) (c) -2…

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

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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: Determine: If W = the set of all vectors in R2 whose second component is the square of the first. is…

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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: Let W be the subspace of P3 spanned by {t³ +t² – 2t + 1, t² + 1, t³ – 2t, 2t³ + 3t² – 4t + 3}. Find…

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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: Find a basis for the subspace а : a, b, c, d E R with 3a + b=0 and c+ d = 0 C W = 6. 6. d of R4.

A: Since 3a+b=0 Therefore b= -3a  And since  c+d=0  Therefore d= -c

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

A: We will solve a system not equations to find the B-coordinate vector. The detailed solution is as…

Q: Find the orthogonal complement S⊥ of the subspace S of R3 spanned by the two column vectors of the…

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Q: . Is the set of all vectors of the form b where a, b, and c are any real numbers with a +b+c> 0, a…

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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: Let W be the subspace spanned by the given vectors. Find a basis for W-. 1 -1 1 W1 W2 -5 -2 1

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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: 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: 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: Find an orthogonal basis of the subspace of spanned by the vectors 日 目 3. (a) (b) (c) (d) 30 123 34

A: Find the orthogonal basis.

Q: {[:} 5. (a) Consider the subspace W = span and consider the vector -1 1 u = -1 |. Find the vector w…

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Q: 2. Is the set of vectors of the form a b a+2b a subspace of R³? Show your proof.

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Q: Find an orthogonal basis of the subspace of spanned by the vectors 旧部。 。 (a) (b) (c) (d) 30 18 123…

A: We have to solve given problem:

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: Let W be the subspace spanned by the given vectors. Find a basis for W⊥

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Q: Find the dimension of the subspace of all vectors in R'whose second and third entries are equal. O…

A: Dimension of subspace is 6. Since dimension of R^7 is 7 and the given subspace has second and third…

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: Let H be the subspace of R with basis B = 3. and let x = 10 6. Is xa vector in H? 14 fx is in H,…

A: Given H is a subspace of R3 with basis {204,231}And x=10614To check x is in H

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: Prove that the the solution to the equation 2x – y+z= 0 is a subspace of R³.

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Q: Find the subspace generated by the vectors A= (2,1,-5), B= (4,3,7) %3D %3D So in space R³

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Q: Let H be the set of all vectors of the form 3s . Find a vector v in R3 such that H = Span {v}. Why…

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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: 2r Let U = |r,s eR Then U is a subspace of R3. %3D .3s Find a basis of U, and calculate dim(U).

A: We have given U=2r-r3s|r,s∈ℝ Then, 2r-r3s=r2-10+s003 Therefore, we can write any vector of U in the…

Q: Consider a subspace and a vector (:) (3) 1 H = Span- 2 X = %3D 2 7 Determine if x e H. If so find…

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Q: Find a basis for the subspace W = {(a,b,c) ∈ R3 | b = 2a−3c}.

A: Given below the detailed solution

Q: Let W be the subspace of IR spanned by the vectors and -6 7 Find the matrix A of the orthogonal…

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Q: Let U={p E p2 : p(2)=0}.Show that U is a subspace of p2 and find a basis for U.

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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: Let W be the subspace spanned by the given vectors. Find a basis for Wt. W = W2 = -5

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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 b1…

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Q: Investigate the dimension of the following subspace of R*. All vectors of the form (a,b,c,d), where…

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Q: Q7) Find a basis for the subspace and state the dimension.  {[2c a − b b − 3c a + 2b]:a, b, c in…

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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.