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3. Let = (1,0, -3). Consider the set of matrices W = {A € M(3, 3) : Au = 0}. %3D (a) Show that W is a subspace of M(3, 3). (b) Find a basis for W.

3. Let = (1,0, -3). Consider the set of matrices W = {A € M(3, 3) : Au = 0}. %3D (a) Show that W is a subspace of M(3, 3). (b) Find a basis for W.

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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13 14 15 16 (a) Give, in order, the clementary matrices of type 3 (i.c. 'shcars' based on row R; + tR;) uscd to reduce A to upper-triangular form. (b) Using (a), find an LU-dccomposition of A. 3. Let = (1,0,-3). Consider the set of matriccs W = {A E M(3,3) : Au = 0}. (a) Show that W is a subspace of M(3,3). (b) Find a basis for W. 4. Consider V = R² with the usual vector addition and thc following strange scalar multiplications (a), (b), (c) shown below. For cach onc, show that V docs NOT form a vector space over R by identifying a problematic axiom from the list V1-V10. Give explicit values for scalars and vectors to show your axiom fails. (a) c*(x1,r2) = (cr1,0) (b) c (T1,12) = (x1, Cr2) S(0,0) if c= 0, Live 35% arch
Transcribed Image Text:13 14 15 16 (a) Give, in order, the clementary matrices of type 3 (i.c. 'shcars' based on row R; + tR;) uscd to reduce A to upper-triangular form. (b) Using (a), find an LU-dccomposition of A. 3. Let = (1,0,-3). Consider the set of matriccs W = {A E M(3,3) : Au = 0}. (a) Show that W is a subspace of M(3,3). (b) Find a basis for W. 4. Consider V = R² with the usual vector addition and thc following strange scalar multiplications (a), (b), (c) shown below. For cach onc, show that V docs NOT form a vector space over R by identifying a problematic axiom from the list V1-V10. Give explicit values for scalars and vectors to show your axiom fails. (a) c*(x1,r2) = (cr1,0) (b) c (T1,12) = (x1, Cr2) S(0,0) if c= 0, Live 35% arch
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