Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Please Solve RD Sharma Class 12 Chapter 6 Adjoint and Inverese of Matrices Exercise 6.1 Question 23 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter 6 Adjoint and Inverese of Matrices Exercise 6.1 Question 23 Maths Textbook Solution.

Answers (1)

best_answer

Answer:

A^{-1}=\left[\begin{array}{cc} 6 & -5 \\ -7 & 6 \end{array}\right]

Hint:

Here, we use basic concept of determinant and inverse of matrix

A^{-1}=\frac{1}{|A|} \times \operatorname{Adj}(A)

Given:

A=\left[\begin{array}{ll} 6 & 5 \\ 7 & 6 \end{array}\right]

Solution:

\begin{aligned} &A^{2}-12 A+I=0 \\\\ &A^{2}=\left[\begin{array}{ll} 6 & 5 \\ 7 & 6 \end{array}\right]\left[\begin{array}{ll} 6 & 5 \\ 7 & 6 \end{array}\right]=\left[\begin{array}{cc} 36+35 & 30+30 \\ 42+42 & 35+36 \end{array}\right]=\left[\begin{array}{cc} 71 & 60 \\ 84 & 71 \end{array}\right] \end{aligned}

Now,

\begin{aligned} &A^{2}-12 A+1=0 \\\\ &{\left[\begin{array}{ll} 71 & 60 \\ 84 & 71 \end{array}\right]-12\left[\begin{array}{ll} 6 & 5 \\ 7 & 6 \end{array}\right]+\left[\begin{array}{ll} 1 & 0 \\ 0 & 1 \end{array}\right]} \\\\ &=\left[\begin{array}{cc} 71-72+1 & 60-60+0 \\ 84-89+0 & 1-72+1 \end{array}\right]=\left[\begin{array}{ll} 0 & 0 \\ 0 & 0 \end{array}\right] \end{aligned}

Also, 

\begin{aligned} &A^{2}-12 A+1=0 \\\\ &A-12 I+A^{-1}=0 \\\\ &A^{-1}-12 I=A \end{aligned}                                                 

\begin{aligned} &A^{-1}=\left[\begin{array}{cc} 12 & 0 \\ 0 & 12 \end{array}\right]-\left[\begin{array}{ll} 6 & 5 \\ 7 & 6 \end{array}\right]=\left[\begin{array}{cc} 12-6 & -5 \\ -7 & 12-6 \end{array}\right] \\\\ &A^{-1}=\left[\begin{array}{cc} 6 & -5 \\ -7 & 6 \end{array}\right] \end{aligned}

Posted by

infoexpert27

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE Class 10, 12 board exams 2025 from April 7 to 11 for sports students
anam-khan

CBSE Class 12 history paper 2025 moderately difficult, tested students’ understanding
anam-khan

CBSE Class 12 Computer Science Exam Analysis 2025: Paper 'moderate', but 'tougher' than last three years

Latest Question