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please Evergreen post complete solution of gbd I am so confused
Allah gives u long live
LINEAR ALGEBRA MTH_501
GDB
Question 1:
Standard basis vectors for are and. If we want to insert into this Basis, then which vector from Standard basis can be removed while still maintaining the Basis of.
Discuss the cases when:
(i) =
(ii) =
Interpret the result geometrically in both cases.
Solution:
(i) will maintain basis of on removal of any of vector from standard basis as each set will form independent set.
Remove v1
Using echelon form
Hence u=0, y=0, z=0 therefore set is independent
Linearly independent as (4, 3, 6) does not lies b\w (0, 0, 1) and (0, 1, 0)
Remove v2
x+4u=0, u=0, z=0 therefore x=0, u=0, z=0. Set is independent
Linearly independent as (4, 3, 6) does not lies b\w (1, 0, 0) and (0, 0, 1)
Remove v3
x+4u=0, y+3u=0, u=0 therefore x=0, y=0, u=0. Set is independent
Linearly independent as (4, 3, 6) does not lies b\w (1, 0, 0) and (0, 1, 0)
(ii) will maintain basis of only on removal of and vector from standard basis, but vector will not maintain basis of .On the removal of vector will form dependent set.
Remove v1
Using echelon form
Hence u=0, y=0, z=0 therefore set is independent
Linearly independent as (4, 0, 6) does not lies b\w (0, 0, 1) and (0, 1, 0)
Remove v3
x+4u=0, 6u+z=0, x=2/3z, u=x/-4, z=3/2x. Set is dependent
Linearly dependent as (4, 0, 6) lies b\w (1, 0, 0) and (0, 0, 1)
Remove v3
x+4u=0, y=0, u=0 therefore x=0, y=0, u=0. Set is independent
Linearly independent as (4, 0, 6) does not lies b\w (1, 0, 0) and (0, 1, 0)
Very Nice.. Gud Effort..its 100% correct solution.
apka solution kaafi helpful or exact hai but apny late upload kya tha so i couldn't gain any benefit from it... :(
Good Luck!!
malika api, is it correct or the upper solution is correct? plz hurry
kindly ab jald az jald isay complete kr lein..
Best of Luck to all of U..!
I think babr ka sahi he
ye solution ha
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