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Which of the following must be true? ) Let V = {(x, y) : x, yeR}For any (x1,Y1), (x2, Y2)eV and c eR, we have (¤1, Y1) + (x2, Y2)= (x1 + x2, Y1 – c (x1, y1) = (cx1, cx2) Then V is a 2-dimensional vector space over R. The set of all n × nmatrices having trace equal to zero is a subspace of Mnxn (R) If Mis a linearly dependent set, then every vector in Mis a linear combination of other vectors in M. O If Vị and V2 are two distinct subspaces of the vector space V, then so is V U V2 For any two (3x3) matrices A and B, we must have (A+ B)² = A² + 2AB+ B2

Which of the following must be true? ) Let V = {(x, y) : x, yeR}For any (x1,Y1), (x2, Y2)eV and c eR, we have (¤1, Y1) + (x2, Y2)= (x1 + x2, Y1 – c (x1, y1) = (cx1, cx2) Then V is a 2-dimensional vector space over R. The set of all n × nmatrices having trace equal to zero is a subspace of Mnxn (R) If Mis a linearly dependent set, then every vector in Mis a linear combination of other vectors in M. O If Vị and V2 are two distinct subspaces of the vector space V, then so is V U V2 For any two (3x3) matrices A and B, we must have (A+ B)² = A² + 2AB+ B2

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Which of the following must be true? Let V = {(x, y) : x, yeR}For any (x1, Y1) , (x2, Y2)eV and c eR, we have (x1, Y1) + (x2, Y2= (x1 + x2, Y1 – Y2ànd c (x1, y1) = (cx1, cx2) Then V is a 2-dimensional vector space over R. The set of all n × nmatrices having trace equal to zero is a subspace of Mnxn (R) O If Mis a linearly dependent set, then every vector in Mis a linear combination of other vectors in M. If Vị and V2 are two distinct subspaces of the vector space V, then so is Vi U V2 O For any two (3x3) matrices Aand B, we must have (A + B)² = A² + 2AB+B²
Transcribed Image Text:Which of the following must be true? Let V = {(x, y) : x, yeR}For any (x1, Y1) , (x2, Y2)eV and c eR, we have (x1, Y1) + (x2, Y2= (x1 + x2, Y1 – Y2ànd c (x1, y1) = (cx1, cx2) Then V is a 2-dimensional vector space over R. The set of all n × nmatrices having trace equal to zero is a subspace of Mnxn (R) O If Mis a linearly dependent set, then every vector in Mis a linear combination of other vectors in M. If Vị and V2 are two distinct subspaces of the vector space V, then so is Vi U V2 O For any two (3x3) matrices Aand B, we must have (A + B)² = A² + 2AB+B²
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