5. the dimension. For each of the following subspaces WC R³, find a basis and determine (a) W = N(A), where (b) W = span S, where A = 1 2 (9) 1 12 235 S = = {(1, 0, 1), (2, 1, 1), (−1, −1,0), (1, 2, -1)}.

Q: The vector x is in a subspace H with a basis B = {b₁,b2}. Find the B-coordinate vector of x. 1 -2 -6…

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Q: 3. The plane in ' with equation 4x=34 %3D

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Q: 11. Find a basis of the following subspace of R4. all vectors of the form (a, b, c, d) where a + b –…

A: The solution is given as

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: 11. Find a basis of the following subspace of R4. W = all vectors of the form (a, b, c, d) where a +…

A: To find: Basis of W={(a,b,c,d) | a+b-c+d=0}.

Q: For the subspace below, (a) find a basis, and (b) state the dimension 9a + 18b-3c 12a-4b-4c - 3a +…

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

A: The orthogonal complement of the subspace W is the set W⊥=v∈V : v, w=0 for all w∈W and the…

Q: 1. Let H be the subspace of RS defined by: 1 1 2 2 3 H = span -2 2 %D 3 -4 4 2 а. Find a basis B of…

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Q: Let v₁ = (-2, 1, 0, -1), v₂ = (0, 1, -2, 1), and b = (1,5,-1, -7). Let W be the subspace or R4…

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Q: s) Determine if these vectors for a basis for R³: linear combination of these vectors. 0·0-0--0- and…

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Q: Let U and W be the sub subspaces of R° generated by the following set vectors respectively. Find the…

A: Sub Space U: Since (2, 9, 0, -5, -2)=-1(1, 3, -3, -1, -4) + 3(1, 4, -1, -2, -2) And (1, 3, -3, -1,…

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: 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: Determine whether U is a subspace of R³. U = {(2r, –s²,t)lr,s, and t E R}

A: Vector Subspace Test: A non-empty subset W of a vector space V is a vector subspace of V if and only…

Q: Find all values of h such that vector y will be in the subspace of R spanned by vectors 3. V1, V2,…

A: we will first find the equivalent matrix and then reduce it to row echelon form

Q: #6. Let W be the subspace of R³ spanned by the two vectors (1, – 1,1) and (3, – 2,0). Which one 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. 5 *H b₁…

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Q: Given the d. subspace V={(x,y,z)=R³ | 2x+y-z=0} of the d. space (R³(R),+,-) and the vector…

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Q: Determine whether the vectors w₁ = [2,1,–3], w₁ = [4,0,2], and w3 = [2,-1,3] form a basis for the…

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Q: Consider the subspace of P2 given by V = span ({-1+r+x²,1– 2r +r, -1+ 3r, 2 – 3r}). Answer the…

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Q: Let A = {(1, –2,0), (0,0, 1), (-1, 2,0)}. Determine if A spans R. If A does not span R°, give a…

A: To find wheather A spans R3 we have to check if it forms a basis in R3

Q: 3. Find the set of vectors in R³ which are orthogonal to both (4, 2, 0) and (3,6,9).

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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: 3. Let W = ((1,2,3,6), (4,–1,3,6), (5, 1, 6, 12)) %3D W2 = ((1,-1,1,1), (2,-1,4, 5)) %3D be…

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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…