Home  18.013A  Chapter 32  Section 32.3 


Find the inverse to the matrix B whose rows are first (2 4); second (1 3).
Solution:
Here are the rows of the matrices starting with B and with I at each stage of the computation,
Start = stage 0
row 1 of B: (2, 4) row 1 of I: (1, 0)
row 2 of B: (1, 3) row 2 of I: (0, 1)
Step 1: divide row 1 by 2
row 1 of B: (1, 2) row 1 of I: (1/2, 0)
row 2 of B: (1, 3) row 2 of I: (0, 1)
Step 2: subtract row 1 from row 2 and replace row 2 by the result
row 1 of B: (1, 2) row 1 of I: (1/2, 0)
row 2 of B: (0, 1) row 2 of I: (1/2, 1)
Step 3: subtract twice row 2 from row 1 and replace row 1 by the result
row 1 of B: (1, 0) row 1 of I: (3/2, 2)
row 2 of B: (0, 1) row 2 of I: (1/2, 1)
