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# MTH501 Graded Discussion Board (GDB) Opening Date 15/7/2014 Closing Date 23/7/2014

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welcome bro... :)

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)

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Very Nice.. Gud Effort..its 100% correct solution.

Babar Bilal

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

thank u very much for sharing

kindly ab jald az jald isay complete kr lein..

Best of Luck to all of U..!

in main say konsa solution teek hai?

I think babr ka sahi he

ye solution ha

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