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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 ,...

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 , – 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

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