4.32: Untitled Page 87

Chapter 4

(1) Construct the augmented matrix AI according to

and use elementary row operations to transform this augmented matrix to the form

Show that the elements represented by B make up the matrix B having the



property that

1

B  A

. Use your result to calculate

1



u  A

b .



(2) Show that the inverse found in Part 1 satisfies

1

A A

 I.

(3) Use Mathematica’s built‐in function Inverse to find the inverse of A .

(4) Use Mathematica’s RowReduce function on the augmented matrix Ab and show that from the row echelon form you can obtain the same results as in (1).

(5) Use Mathematica’s Solve function to solve Au  b .