MA371 Worksheet March 30, 2001

These exercises should be worked on for Monday.

1


    ( 1  0   1 )
A = ( 0  1  -3 )
    ( 2  3  -8 )

Determine the rank of A. Find a basis for the row space of A. Find a basis for the column space of A. Find a basis for the nullspace of A.

2

     ( 1  2  0   0   1   0  0 )         ( 1 )
     ( 3  6  1  -3   1   2  6 )         ( 0 )
A =  ( 2  4  1  -2   8   6  2 )    b =  ( 0 )
     ( 6 12  2  -5   9   8  8 )         ( 1 )
     ( 1  2  0  -1  -7  -4  4 )         ( 1 )

Determine the rank of A. Find a basis for the row space of A. Find a basis for the column space of A. Find a basis for the nullspace of A.
Doe the equation Ax= b have a solution? If so, describe the set of all solutions. If not, change the last element b₅ to a number so that the system is solvable.

3

                            ( 1  0  0  0 )
    ( 1  0  2  0  0 )       ( 0  1  0  0 )
A = ( 0  1  0  1  0 )   B = ( 0  0  0  1 )
    ( 0  0  0  0  1 )       ( 0  0  0  0 )
                            ( 1  1  1  1 )

Determine AB. Find the rank of AB. Find a basis for the nullspace of AB. Find a basis for the nullspace of B. Find a basis for the column space of A. What vectors are in the intersection of the nullspace of B and the column space of A?

Section 3.6 #10

Section 3.6 #13

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