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Which of the following must be true? If Mis a linearly dependent set, then every vector in Mis a linear combination of other vectors in M. For any two (3x3) matrices A and B, we must have (A + B)² = A² + 2AB+ B² Let V = {(x, y) : x, yeRFor any (x1, Y1), (x2, Y2 )eV and c eR, we have (x1, Yı) + (x2, Y2} (x1 + x2, Y1 – Y2) and c (x1, Yı) = (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 V, and V, are two distinct subspaces of the vector space V, then so is Vị u V2

Which of the following must be true? If Mis a linearly dependent set, then every vector in Mis a linear combination of other vectors in M. For any two (3x3) matrices A and B, we must have (A + B)² = A² + 2AB+ B² Let V = {(x, y) : x, yeRFor any (x1, Y1), (x2, Y2 )eV and c eR, we have (x1, Yı) + (x2, Y2} (x1 + x2, Y1 – Y2) and c (x1, Yı) = (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 V, and V, are two distinct subspaces of the vector space V, then so is Vị u V2

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? O If Mis a linearly dependent set, then every vector in Mis a linear combination of other vectors in M. For any two (3x3) matrices A and B, we must have (A + B)² = A² + 2AB+B² O Let V = {(x, y) : x, yeRFor any (x1, Y1) , (x2, Y2 EV and c eR, we have (x1, Y1) + (x2, Y2} (X1 + x2, Y1 – Y2) and c (x1, Y1) = (cx1, cx2)Then V is a 2- dimensional vector space over R. %3D The set of all n × nmatrices having trace equal to zero is a subspace of Mnxn (R) O If Vi and V2 are two distinct subspaces of the vector space V, then so is Vị U V2
Transcribed Image Text:Which of the following must be true? O If Mis a linearly dependent set, then every vector in Mis a linear combination of other vectors in M. For any two (3x3) matrices A and B, we must have (A + B)² = A² + 2AB+B² O Let V = {(x, y) : x, yeRFor any (x1, Y1) , (x2, Y2 EV and c eR, we have (x1, Y1) + (x2, Y2} (X1 + x2, Y1 – Y2) and c (x1, Y1) = (cx1, cx2)Then V is a 2- dimensional vector space over R. %3D The set of all n × nmatrices having trace equal to zero is a subspace of Mnxn (R) O If Vi and V2 are two distinct subspaces of the vector space V, then so is Vị U V2
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