2.2soln

# 2.2soln - Solutions to even problems from section 2.2 2...

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

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

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

Unformatted text preview: Solutions to even problems from section 2.2 2. Find the inverse of the matrix bracketleftbigg 3 2 7 4 bracketrightbigg . Solution: Since det bracketleftbigg 3 2 7 4 bracketrightbigg = 3(4) − 7(2) = − 2 we have bracketleftbigg 3 2 7 4 bracketrightbigg- 1 = − 1 2 bracketleftbigg 4 − 2 − 7 3 bracketrightbigg = bracketleftbigg − 2 1 7 / 2 − 3 / 2 bracketrightbigg 8. Use matrix algebra to show that if A is invertible and D satisfies AD = I , then D = A- 1 . Solution: Since A is invertible we know A- 1 exists. Thus we have D = ID = ( A- 1 A ) D = A- 1 ( AD ) = A- 1 I = A- 1 . 10. True or false? Justify your answer. a. A product of invertible n × n matrices is invertible, and the inverse of the product is the product of their inverses in the same order. Solution: FALSE. For example, if we let A = bracketleftbigg 1 − 1 bracketrightbigg , and B = bracketleftbigg 1 0 1 1 bracketrightbigg then we have ( AB )- 1 = bracketleftbigg 1 − 1 − 1 bracketrightbigg- 1 = bracketleftbigg...
View Full Document

## This note was uploaded on 01/28/2010 for the course MATH 307 taught by Professor Axenovich during the Fall '08 term at Iowa State.

### Page1 / 2

2.2soln - Solutions to even problems from section 2.2 2...

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

View Full Document
Ask a homework question - tutors are online