Join Sarthaks eConnect Today - Largest Online Education Community!
0 votes
8 views
asked ago in Mathematics by (19k points)

Show that the matrix  A = [(2, 3), (1, 2)]  satisfies the equation A2 – 4A + I = O, where I is 2 × 2 identity matrix and O is 2 × 2 zero matrix. Using this equation, find A–1.

1 Answer

+1 vote
answered ago by (21k points)
selected ago by
 
Best answer

Given that

Now, A2 - 4A + I = 0

⇒ AA - 4A = -I

⇒ AA(A-1) - 4AA-1 = - IA-1(Post multiplying by A–1 because |A| ≠ 0)

⇒ A(AA-1) - 4I = - A-1

⇒ AI - 4I = - A-1

Happy Diwali Wishes

Related questions

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

One Thought Forever

“There is a close connection between getting up in the world and getting up in the morning.“
– Anon
~~~*****~~~

Categories

...