Which of the following must be true? OThe set of all n x matrices having trace equal to zero is a subspace of Mnxn (R) OLet V = {(x, y) : x, yeR}For any (x1, Y1), (x2, Y2)eV and c eR, we have (æ1, Y1) + (x2, Y2} (x1 + x2, Y1 – Y2) and c (x1, y1) = (cx1, cx2)Then V is a 2-dimensional vector space over R. For any two (3x3) matrices A and B, we must have (A + B)? = A² + 2AB+ B2 Olf M is a linearly dependent set, then every vector in M is a linear combination of other vectors in M. Olf Vị and V2 are two distinct subspaces of the vector space V, then so is V1 U V2

Which of the following must be true? OThe set of all n x matrices having trace equal to zero is a subspace of Mnxn (R) OLet V = {(x, y) : x, yeR}For any (x1, Y1), (x2, Y2)eV and c eR, we have (æ1, Y1) + (x2, Y2} (x1 + x2, Y1 – Y2) and c (x1, y1) = (cx1, cx2)Then V is a 2-dimensional vector space over R. For any two (3x3) matrices A and B, we must have (A + B)? = A² + 2AB+ B2 Olf M is a linearly dependent set, then every vector in M is a linear combination of other vectors in M. Olf Vị and V2 are two distinct subspaces of the vector space V, then so is V1 U V2

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.6: Rank Of A Matrix And Systems Of Linear Equations

Problem 67E: Let A be an mn matrix where mn whose rank is r. a What is the largest value r can be? b How many...

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