Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
368 views
in Matrices by (25.7k points)
closed by

Let \(F(\alpha)=\begin{bmatrix}cos\alpha&-sin\alpha&0\\sin\alpha&cos\alpha&0\\0&0&1\end{bmatrix}\) and \(G(\beta)\begin{bmatrix}cos\beta&0&sin\beta\\0&1&0\\-sin\beta&0&cos\beta\end{bmatrix}\)

Show that [G(β)] –1 = G( – β)

1 Answer

+1 vote
by (27.7k points)
selected by
 
Best answer

\(G(\beta)\begin{bmatrix}cos\beta&0&sin\beta\\0&1&0\\-sin\beta&0&cos\beta\end{bmatrix}\)

|G(β)| = \(cos^2\beta+sin^2\beta\) = 1

Cofactors of A are:

C11 = cosβ C21 = sinα C31 = sinβ

C12 = 0 C22 = 1 C32 = 0

C13 = sinβ C23 = 0 C33 = cosβ

Hence, [G (β)] –1 = G( – β)

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.

...