Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Find the inverse of each of the matrices (if it exists). Q:5 Matrix 2 -2 4 3

Q : 5          Find the inverse of each of the matrices (if it exists).

                   \small \begin{bmatrix} 2 &-2 \\ 4 & 3 \end{bmatrix}

Answers (1)

best_answer

Given matrix :  \small \begin{bmatrix} 2 &-2 \\ 4 & 3 \end{bmatrix}

To find the inverse we have to first find adjA then as we know the relation:

A^{-1} = \frac{1}{|A|}adjA

So, calculating |A| :

|A| = (6+8) = 14

Now, calculating the cofactors terms and then adjA.

A_{11} = (-1)^{1+1} (3) = 3

A_{12} = (-1)^{1+2} (4) = -4

A_{21} = (-1)^{2+1} (-2) = 2

A_{22} = (-1)^{2+2} (2) = 2

So, we have adjA = \begin{bmatrix} 3 &2 \\ -4& 2 \end{bmatrix}

Therefore inverse of A will be:

A^{-1} = \frac{1}{|A|}adjA

= \frac{1}{14}\begin{bmatrix} 3 &2 \\ -4& 2 \end{bmatrix} = \begin{bmatrix} \frac{3}{14} &\frac{1}{7} \\ \\ \frac{-2}{7} & \frac{1}{7} \end{bmatrix}

 

Posted by

Divya Prakash Singh

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

PM Modi's Pariksha Pe Charcha 2025 to be held next month, registrations open till January 14
anam-khan

CBSE Board Exams 2025: Online portal for availing exemptions by CWSN students opens
anam-khan

Board Exams: States agree to equivalence; no question paper ‘jumbling’ from next year, says PARAKH CEO

Latest Question