In the space R^4, two subspaces are given: U={(a,b,c,d)∈R^4 ∣ a+b=0, b+c=0, c+d=0} and V={(a,b,c,d)∈R^4 ∣ a+c=0, a+d=0}. What is the dimension of the intersection of U and V?
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In the space R^4, two subspaces are given: U={(a,b,c,d)∈R^4 ∣ a+b=0, b+c=0, c+d=0} and V={(a,b,c,d)∈R^4 ∣ a+c=0, a+d=0}. What is the dimension of the intersection of U and V?
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- Determine: if W = the set of all vectors in R^2 whose second component is the square of the first. Is a subspaceWhich of the following sets of vectors spans R^2? A. {(1, 1), (–2, –2)} B. {(1, 1), (1, 2)} C. {(1, 2), (0,0)} D. {(–1, 1), (1, –1)}In the space R^4, two subspaces are given: U={(a,b,c,d)∈R^4∣a+b=0,b+c=0,c+d=0} and V={(a,b,c,d)∈R^4∣a+c=0,a+d=0}. What is the dimension of the intersection of U and V? (a) 0. (b) 1. (c) 2. (d) 3. (e) 4.
- Write the equation of a subspace that passes through a point a ∈ R^d and isorthogonal to a given vector b. What is that equation for d = 3, d = 2?Consider a set of vectors of the form (a,3a, a+b). Determine whether the set is a subspace of R^3 If the set is a subspace, give a basis and its dimension.Why is this set not a subspace of R^3? W = { (a1, a2, a3) : a22 = a1 - a3 } ( the two 2s are supposed to be directly over/under each other)
- Is the set of vectors of the form [a,b,a+2b] a subspace of R^3Determine whether the set of vectors is a basis for the subspace of R^n that the vectors span. Please explain why or why not and what exactly a "basis" is somewhere in answer/response.Express the vector (-1,5,-6) in R^3as a linear combination of (2,0,7),(2,4,5) and (2,-12,13).
- of set ℝ^? Show whether or not is a subspace.Determine whether the set S spans R^2. If the set does not span R^2, then give a geometric description of the subspace that it does span.Suppose V,W are subspaces of R^n. Let V ∩ W be all vectors which are in both V andW. Show that V ∩W is a subspace also.