solhw7 - Solutions to Homework#7 MAT1341A Question 1(2 2 =...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Solutions to Homework #7, MAT1341A Question # 1: (2+2 = 4 points) Simplify the following expressions, if possible. Assume all matrices are n × n and invertible. (a) ( ABA- 1 A ) T B- 1 Solution: ( ABA- 1 A ) T B- 1 = ( ABI ) T B- 1 = ( AB ) T B- 1 = B T A T B- 1 (b) (( AB ) T )- 1 Solution: (( AB ) T )- 1 = ( B T A T )- 1 = ( A T )- 1 ( B T )- 1 Question # 2: (3+3+3+3+3 = 15 points) Find the inverses of each of the following matrices, if they exist. If they are not invertible, explain why not. If they are invertible, check your answer by multiplying AA- 1 . (Continued on next page.) (a) A = 6 1 20 1 3 4- 3 8 Solution: 6 1 20 1 1 3 1 4- 3 8 1 ----→ R 1 R 2 1 3 1 6 1 20 1 4- 3 8 1 R 2 → R 2- 6 R 1-------→ R 3 → R 3- 4 R 1 1 3 1 1 2 1- 6- 3- 4- 4 1 -------→ R 3 → R 3 +3 R 2 1 3 1 1 2 1- 6 2 3- 22 1 -----→ R 3 → 1 2 R 3 1 3 1 1 2 1- 6 1 3 2- 11 1 2 R 2 → R 2- 2 R 3-------→ R 1 → R 1- 3 R 3 1- 9 2 34- 3 2 1- 2 16- 1 1 3 2- 11 1 2 On the left hand side, we got I , so the inverse exists and it’s on the right hand side. A- 1 = - 9 2 34- 3 2- 2 16- 1 3 2- 11 1 2 Check: 6 1 20 1 3 4- 3 8 - 9 2 34- 3 2- 2 16- 1 3 2- 11 1 2 = 1 1 1 - 9 2 34- 3...
View Full Document

{[ snackBarMessage ]}

Page1 / 3

solhw7 - Solutions to Homework#7 MAT1341A Question 1(2 2 =...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online