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-2 -4 Let A-5 8 -2 and b = -2 -5 (a) Determine if b is a linear combination of a1, az and an, the columns of the matrix A. (b) If it is a linear combination, determine a non-trivial linear relation - (a non- trivial relation is three numbers which are not all three zero.) Otherwise, enter O's for the coefficients. a=b. ai+ a2+

-2 -4 Let A-5 8 -2 and b = -2 -5 (a) Determine if b is a linear combination of a1, az and an, the columns of the matrix A. (b) If it is a linear combination, determine a non-trivial linear relation - (a non- trivial relation is three numbers which are not all three zero.) Otherwise, enter O's for the coefficients. a=b. ai+ a2+

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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-2 -4 -6 1. Let A = 5 -2 and b = 18 -2 -5 (a) Determine if b is a linear combination of a1, a2 and a3, the columns of the matrix A. (b) If it is a linear combination, determine a non-trivial linear relation - (a non- trivial relation is three numbers which are not all three zero.) Otherwise, enter O's for the coefficients. aj+ a2+ a3 = b. 2. Let (a) Are the vectors v'1, v2, and v'a linearly independent? (b) If the vectors are independent, enter zero in every answer blank since those are only the values that make the equation below true. If they are dependent, find numbers, not all zero, that make the equation below true. You should be able to explain and justify your answer. 3. v'i= (1-2), v*2= (-5,3), v*s= (22,-9). (a) Are the vectors v'1, v 2, and v'3 linearly independent? (b) If the vectors are independent, enter zero in every answer blank since zeros are only the values that make the equation below true. If they are dependent, find numbers, not all zero, that make the equation below true. You should be able to explain and justify your answer. (0,0)= (1,-2)+ (-5,3)+ (22,-9). 4. Let vi=(12,4,20), v"2=(6,-6,6), v'3=(12,0,18). (a) Are the vectors v'1, v 2, and v'a linearly independent? (b) If the vectors are independent, enter zero in every answer blank since those are only the values that make the equation below true. If they are dependent, find numbers, not all zero, that make the equation below true. You should be able to explain and justify your answer. (0,0,0)= (12,4,20)+ (6,-6,6)+ (12,0,18).
Transcribed Image Text:-2 -4 -6 1. Let A = 5 -2 and b = 18 -2 -5 (a) Determine if b is a linear combination of a1, a2 and a3, the columns of the matrix A. (b) If it is a linear combination, determine a non-trivial linear relation - (a non- trivial relation is three numbers which are not all three zero.) Otherwise, enter O's for the coefficients. aj+ a2+ a3 = b. 2. Let (a) Are the vectors v'1, v2, and v'a linearly independent? (b) If the vectors are independent, enter zero in every answer blank since those are only the values that make the equation below true. If they are dependent, find numbers, not all zero, that make the equation below true. You should be able to explain and justify your answer. 3. v'i= (1-2), v*2= (-5,3), v*s= (22,-9). (a) Are the vectors v'1, v 2, and v'3 linearly independent? (b) If the vectors are independent, enter zero in every answer blank since zeros are only the values that make the equation below true. If they are dependent, find numbers, not all zero, that make the equation below true. You should be able to explain and justify your answer. (0,0)= (1,-2)+ (-5,3)+ (22,-9). 4. Let vi=(12,4,20), v"2=(6,-6,6), v'3=(12,0,18). (a) Are the vectors v'1, v 2, and v'a linearly independent? (b) If the vectors are independent, enter zero in every answer blank since those are only the values that make the equation below true. If they are dependent, find numbers, not all zero, that make the equation below true. You should be able to explain and justify your answer. (0,0,0)= (12,4,20)+ (6,-6,6)+ (12,0,18).
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