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Mathematics LibreTexts

2.7.1: Exercises 2.7

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In Exercises 2.7.1.1 - 2.7.1.4, matrices A and B are given. Compute (AB)1 and B1A1.

Exercise 2.7.1.1

A=[1211],B=[3525]

Answer

(AB)1=[2311.4]

Exercise 2.7.1.2

A=[1234],B=[7121]

Answer

(AB)1=[7/103/1029/1011/10]

Exercise 2.7.1.3

A=[2538],B=[1114]

Answer

(AB)1=[29/518/511/57/5]

Exercise 2.7.1.4

A=[2425],B=[2265]

Answer

(AB)1=[29/4617/27]

In Exercises 2.7.1.5 - 2.7.1.8, a 2×2 matrix A is given. Compute A1 and (A1)1 using Theorem 2.6.3.

Exercise 2.7.1.5

A=[3512]

Answer

A1=[2513],(A1)1=[3512]

Exercise 2.7.1.6

A=[3524]

Answer

A1=[25/213/2],(A1)1=[3524]

Exercise 2.7.1.7

A=[2713]

Answer

A1=[3712],(A1)1=[2713]

Exercise 2.7.1.8

A=[9079]

Answer

A1=[1/907/811/9],(A1)1=[9079]

Exercise 2.7.1.9

Find 2×2 matrices A and B that are each invertible, but A+B is not.

Answer

Solutions will vary.

Exercise 2.7.1.10

Create a random 6×6 matrix A, then have a calculator or computer compute AA1. Was the identity matrix returned exactly? Comment on your results.

Answer

Likely some entries that should be 0 will not be exactly 0, but rather very small values

Exercise 2.7.1.11

Use a calculator or computer to compute AA1, where

A=[12341491618276411681256].

Was the identity matrix returned exactly. Comment on your results.

Answer

Likely some entries that should be 0 will not be exactly 0, but rather very small values.


This page titled 2.7.1: Exercises 2.7 is shared under a CC BY-NC 3.0 license and was authored, remixed, and/or curated by Gregory Hartman et al..

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