Question (1)

Find a basis and dimension of the subspace W of R4 generated by the vectors

( 1 , - 4 , - 2 , 1 ) , ( 1 , - 3 , - 1 , 2 ) , ( 3 , - 8 , - 2 , 7 ) .

Extend it to find the basis of R4

Question (2)

Determine a basis and the dimensions of the Subspace of M2(R) generated by the

2 by 2 Matrices [ 2 -10 ] , [ 3 3 ] , [ 2 -4 ] , [ 2 -14 ]

[ -8 4 ] [ -3 15] [ -5 7] [ -10 2 ]

NOTE : For the full description of the question in mathematical font and format, please download the attached question file.

Question (1)

Find a basis and dimension of the subspace W of R4 generated by the

vectors

( 1 , â 4 , â 2 , 1 ) , ( 1 , â 3 , â 1 , 2 ) , ( 3 , â 8 ,

â 2 , 7 ) .

Extend it to find the basis of R4

Question (2):

Determine a basis and the dimensions of the Subspace of M2(R) generated

by the

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