Linear Algebra: Multiplication by Special Matrices

[robbie11]

Im working on this problem and got stuck i would appreciate any help...

Let Eij be the n × n matrix with 1 at the (i, j)th place and zero elsewhere.
For a scalar c in K, put S = I + cEij . And let T be the n × n
matrix obtained from the identity matrix as follows. In I replace 1 at
the (i, i)th and (j, j)th entries by zero. Replace zeros at the (i, j)th and
(j, i)th entry by 1. Suppose A is an n × n matrix. Compute SA, AS,
TA, and AT to conclude what does the multiplication on the left or
right by S or T do to the row or columns of A.

robbie

 

[tiny-tim]

Welcome to PF!

Hi robbie! Welcome to PF!:

(try using the X₂ tag just above the Reply box )

Show us what you've tried, and where you're stuck, and then we'll know how to help!

(if you want to write the matrices out, either use the CODE tag, 3 to the left of the X₂ tag, or use LaTeX and http://www.physics.udel.edu/~dubois/lshort2e/node54.html#SECTION00830000000000000000" )