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

Q: (2) Find a basis for the subspace W = {(a+c,2a – 6, 3a – 26 – c, b + 2c) | a, b, c E R} of R4

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Q: Find a basis for the subspace of R3 spanned by S = {(2,3, -1), (1,3, -9), (0,1,5)}

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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: 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: 1. For each of the following matrices, determine a basis - and N(A"): 4 subspaces R(A"), N(A), R(A),…

A: Let us apply elementary row operations on the given Matrix A to reduce it in reduced row Echelon…

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: The set B=(v= (1,1,1),u=(0,0, - 3),w=(2,2,0)) IS: OA Linearly independent in R3. OBa subspaces of R.…

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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 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: a Let M = . -b a,b,c e R},N x, y e R} be two subspaces of M2x2. Find the basis for M, N and MON.

A: We will find the bases of M and N. Then we will find the intersection of their basis vectors, which…

Q: Find a basis for the subspace of R3 spanned by S.S = {(1, 2, 4), (−1, 3, 4), (2, 3, 1)}

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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: Find a basis for the subspace of R3 spanned by S.S = {(4, 4, 8), (1, 1, 2), (1, 1, 1)}

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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: Let S=v1,v2,v3,v4, where v1= (1,1,2,1), v2= (1,0,−3,1),v3= (0,1,1,2),v4= (0,0,1,1), and v5=…

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Q: Find a basis for each subspace... [5r-3s, 2r, 0, -4s] ER^4:r and s are scalars

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Q: Find an orthogonal basis of the subspace of spanned by the vectors (a) (b) -2 (c) (d) 234

A: To find the orthogonal basis of the subspace of spanned by the vectors 234 and 123 Consider that the…

Q: Find a basis for the subspace of R^3: sp([1, -3, 2], [2, -5, 3], [4, 0, 1]). Show your work, and…

A: We find basis of subspace of R^3: sp([1, -3, 2], [2, -5, 3], [4, 0, 1]).

Q: 1 2 Find a basis for subspace V of R4 spanned by the vectors 3 dimension of V? 8 What is the

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Q: Let 1 -3 and let W the subspace of R' spanned by u and v. Find a basis of W-, the orthogonal…

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Q: For vectors, v0= (0,3,4,2),v1= (1,1,2,1), v2= (1,0,0,0), v3= (0,0,1,0), find an orthonormal basis,…

A: Solution by using Gram Schmidt process as follows :

Q: 2. Consider the subspace im(A) of Rº, where 1 1 A = | 1 1 3 Find a basis of ker(A"), and draw a…

A: Given matrix A=111213 AT=111123

Q: A base of the subspace W={ (a, b, c); a-2b+c=0} is:

A: According to the question,

Q: Let S be a subspace of V. Starting with a basis {81,..., s} for S, how would you find a basis for…

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Q: Suppose that B = {V₁, V2,..., Vk) is an orthonormal basis for a subspace W of R". Let C be the nx k…

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Q: Find the orthogonal projection of -5 -1 16 onto the subspace W of IR³ spanned by 4 -4 and 2 24 projw…

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Q: 4. Find a basis and the dimension of the subspace W of V = M22(R) spanned by %3D -5 2 -4 A = B = C =…

A: Given:          V = M2 × 2(ℝ) spanned by A = 1-5-42 ; B = 11-15 ; C = 2-4-57 and D = 1-7-51   To…

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: Find a basis and dimension of the subspace described as follows:{(x, y, z, w) |2x + 5y – z=0} (0-0)…

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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: Let 3 u= and let W the subspace of Rª spanned by ū and v. Find a basis of W+, the orthogonal…

A: Given vectors, u→=-3-10-2-2,v→=132-3 The objective is to find the basis of W⊥ the orthogonal…

Q: Find a basis and the dimension of each of the following subspaces of R" a. W1 = v: u + v = 0 and u…

A: Given :  The subspaces of  ℝ3  are given as ; a)   W1 = { (u, v, w) : u+v=0  and u-2w=0 } b)   W2 =…

Q: Given a basis B = {V1, V2,, Vn} of Subspace S, there is a unique way to express any ... vE S as a s…

A: We will first write 2 expressions of v as a linear combination of basis vectors in B. Then, we will…

Q: Find a basis for the subspace of R³ spanned by S. S= {(4,2,-1), (1,2,8), (0,1,2)}

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Q: Find a basis for the following subspace of R°: W3D {(aj + 5а2 — 2а3, 2а1+ 6а2 — аз, Зај + 7а2) : ај,…

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Q: Find a basis for the subspace W p(x) E P2 p(5) = -p(-5)} of P2. A basis for W is { x2 -Ex: 1 , x

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Q: Find the orthogonal projection of -13] 15 onto the subspace W of R4 spanned by 4 and 5 -2 -2…

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Q: 6. a. Give a basis for the orthogonal complement of the subspace V C R' given by V = {x € R* : xị…

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Q: Find the orthogonal projection of [-10] = -15 12 onto the subspace W of IR spanned by 日-日 1 9. and 6…

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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: Find a basis for the subspace of R3 spanned by S.S = {(2, 3, −1), (1, 3, −9), (0, 1, 5)}

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Q: Let A be an m×n matrix. Find all b such that the set of solutions to Ax = b is a subspace and prove.

A: Given: Let A be an m×n matrix.  The objective is to find that the set of solutions to Ax =b is a…

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: 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: In each part, find a basis for the given subspace of R4 (3) All vectors of the form (a, b, c, d)…

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Q: (2) Find a basis of the following subspaces and find their dimensions. a + 2c b — с : а, b, с €R a +…

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Q: The sequence B = (3,5) is a basis for the subspace () -- V = { 22: 2xi + x2 – 13 = 0}. The vector w…

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Q: Find a basis for the Nul subspace spanned by the vectors The basis elements: 2 2 00000

A: Given are the vectors that span a Nul space. The objective is to determine the basis for that Nul…

Q: Find a basis for the subspace of R spanned by the following vectors. 7 4 2 2 18 -3 6 6 18 18 12 14…

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