Which of the following is not a subspace of AW₂ = {(a,b,c,d)|a+b+c+d=1} BW₁ = {(a, a, b, b) | a, b = R} CW₂ = {(a, b, c, d) | a = b, c =d} DW₁ = {(a + b, a, b, 0)| a, b < R}

Q: The set W : 3x - y = z -5w = 0} is a subspace of R*. What is the dimension of W Select one: а. 1 b.…

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Q: Q6) Determine whether the set S spans R³. If the set doesn't span R³, give a geometric description…

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Q: Determine if (x, y, z, t) ∈ R^4 such that y = −x and z = 0, and t = 2x form a subspace of R^4

A: Use the necessary and sufficient condition for a subspace of a vector space

Q: What is the dimension of the subspace or the space of 5 x 5 matrices (ai) sucn that a11 +...+ az5 =…

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Q: What is the matrix P = (P₁) for the projection of R³ onto the subspace V spanned by the vectors a₁ =…

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Q: Why is this set not a subspace of R^3? W = { (a1, a2, a3) : a22 = a1 - a3 } ( the two 2s are…

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Q: Which of the following sets is a basis for the subspace U={(a,b,c,d)∈R4 ∣ a−b=0,a+d=0,b+d=0} in the…

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Q: Determine whether the given set S is a subspace of the vector space V. DA. V = C5 (I), and S is the…

A: A subset S of vector space V is said to be a subspace of V if it is closed under vector addition and…

Q: ніну, зєв 2 Let S = {(u,Y,Z): x+y=} #ny,ZER_ Show that S is a subspace & R3.

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Q: Find a minimal spanning set for the subspace spanned by the set of vectors: S={, , , }

A: The given spanning set is S=1, 0, 0, -1, 4, 4, 0, 0. We have to find the minimal spanning set.

Q: Find a linearly independent set of vectors that spans the same subspace of IR" as that spanned by…

A: The given vectors are                                   -3110, -12613, 3-55-6, -33-23…

Q: 2) One of the following subsets of IR2 is not subspace: a) S = {, xeR} b) s = {], = x3} %3D %3D e) s…

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Q: Find the orthogonal projection of the vector [ 49 49 49] onto the subspaces of R3 spanned by [2 3…

A: We have to find the orthogonal projection of the vector  onto the subspace of  spanned by  and .

Q: 5. Let W be the subspace of the vector space V = R spanned by the vectors =(1,3, 1, -2), B = (-3,…

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Q: Find a linearly independent set of vectors that spans the same subspace of R* as that spanned by the…

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Q: Let U and V be the subset of R' defined as U = { (a,b.c,d) : 3b-2d-a = 0 } and / = { (a,b,c,d) : a=c…

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Q: Find a basis for the subspace of R* spanned by S. S = {(43, -21, 6, 12), (-14, 7, -2, –4), (6, –3,…

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Q: 21 3 Find a basis for the subspace of R³ consisting of all vectors 22 such that 61 - 7x2 - 4x3 = 0.…

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Q: Find a basis for the subspace of R4 spanned by S. S = {(-11, 6, 4, 8), (-6, 3, 2, 4), (-2, 1, 1, 2),…

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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: Find a basis for the subspace of R* spanned by S. S = {(64, -21, 9, 27), (-21, 7, -3, -9), (6, -2,…

A: B is called the basis for the subspace of ℝ4 spanned by S  if i) B is linearly independent  ii) B…

Q: Given that V1 = 5 3 V2 = 2 } V3 = 3 7 " 11 10 For what value(s) of h will y be in the subspace of H…

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Q: Determine whether the given subset is subspace of R^3 W={(x1,x2,x3):x1+x2+x3=0}

A: Let the subset W is given as W={(x1,x2,x3)| x1+x2+x3=0} Determine whether the given subset is…

Q: Let V be the subspace of R' spanned by vi = (1, 3, -2, 2, 3 ), v (1, 4, -3, 4, 2 ), v3 (1, 3, 0, 2,…

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Q: 2. Determine which of the following is a subspace of R". (a) {(x1,x2,...X) 1 x = 0} (b) {(x1,…

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Q: Let W = {(" ):a+ 2c = 0 andb-d 0} be a subspace of M22. %3D Then dimension of W is equal to: O 1…

A: The solution is given in the next step.

Q: Let W be the subspace of IR' spanned by the vectors 1 4 -2 and -1 -7 Find the matrix A of the…

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Q: Vi and V2 be subspaces of R* (over R) Their intersection V=v,nV; is the set of all vectors that lie…

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