(1) Write down the coefficient matrix corresponding to the system
(2) The row echelon form of
is
What is the rank of 
?
How many solutions does the equation
have?
(3) Write the problem of determining whether the vectors
are linearly dependent as a matrix problem involving the matrix
above (see Linear Combination q.3). Use your answer to
(2) to show that these vectors are linearly dependent.
(4) What vectors form the column space of
?
What vectors form the row space of
?
(5) From (2) write down a basis for the column space of
. Do the same for the
row space.
What is the equation relating the column rank, row rank and
rank of a matrix. Verify this for the matrix
using your answers to (2) and (5).