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J.M.Patel Arts,Commerce & Science College Bhandara-441904
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Q.1 Let V be a vector space with dimension 12. Let S be a subset of V which is linearly independent and has 11 vectors. Which of the following is FALSE?
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Q.2 Let T be a Linear map from U to V & T is 1-1 then
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Q.3 Let {u, v, w} be an independent set in a vector space.
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Q.4 A set of linear equations is represented by the matrix equation Ax = b. The necessary condition for the existence of a solution for this system is A.
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Q.5 If a linear transformation from V5 to V3 is onto, then
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Q.6 Let T be a linear transformation from V3 to V5 . Then
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Q.7 If a vector space V is n- Dimensional. Which of the following is FALSE?
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Q.8 If V has a basis of n elements, then every set of m vectors is not linearly independent with
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Q.9 Which of the following subsets of V3 are LI?
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Q.10 The Rank of a 3 × 5 matrix is three.
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Q.11 Let B and D denote two bases of an n-dimensional vector space V.
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Q.12 Let V be a five-dimensional vector space and let S be a subset of V consisting of five vectors. Then S
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Q.13 Let V be a five-dimensional vector space and let S be a subset of V which is linearly dependent. Then S
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Q.14 Let V be a five-dimensional vector space and let S be a subset of V consisting of three vectors. Then S
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Q.15 Let V be a five-dimensional vector space and let S be a subset of V which spans V . Then S
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Q.16 Let V be a vector space and let S be a subset of V. What does it mean when we say that S spans V?
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Q.17 Let V be a five-dimensional vector space and let S be a subset of V which is a basis for V. Then S
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Q.18 Which of the following transformation not linear?
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Q.19 Let I be the identity transformation of the finite dimensional vector space V, then the nullity of I is
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Q.20 Let u, v, w be three non-zero vectors which are linearly independent, then
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Q.21 Let S=2-x+3x^2, x+x^2, 1-2x^2 be subset of P^2(R). Then
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Q.22 U and V are subspace of R^4 such that U = span [(1,2,3,4), (5,7,2,1), (3,1,4,-3)] & V=span [(2,1,2,3), (3,0,1,2), (1,1,5,3)]. Then the dimension of U intersection V is
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Q.23 Which Statement is true?
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Q.24 Every group is isomorphic to a subgroup of A(S) for appropriate S.