Find the inverse of the matrix if it exists. [[-7,4],[8,-5]]

bistandsq

bistandsq

Answered question

2022-01-21

Find the inverse of the matrix if it exists.
[7485]

Answer & Explanation

seibesitoeu

seibesitoeu

Beginner2022-01-22Added 12 answers

Step 1
Inverse of a matrix A denoted by A1 is the matrix such that, 1=A1A=I where I is the identity matrix.
A matrix A has an inverse if and only if its determinant is non-zero.
The inverse of a matrix can be found out by elementary row or elementary column transformations.
Step 2
The given matrix is,
A=[7485]
The determinant of the above matrix is,
|A|=(7×5)(4×8)
=3532
=30
Hence A has an inverse.
Step 3
To find the inverse of A:
A=AI
[[7,4].[8,5]]=A[1001]
R1R1+R2
[7+84585]=A[1+00+101]
[[1,1][8,5]]=A[[1,1][0,1]]
R2R28R1
[1181×85(1)×8]=A[1101×811×8]
[1103]=A[1187]
R2R23
[110333]=A[118373]
[1101]=A[118373]
R1R1+R2
[1+01+101]=A[1831738373]

search633504

search633504

Beginner2022-01-23Added 16 answers

Step 1
Given: (7485)
Find the determinant of the matrix.
det((7485))
For the 2×2 matrix (abcd), the determinant is adbc
7(5)4×8
Multiply -7 times -5
354×8
Multiply 4 times 8
3532
Subtract 32 from 35
Answer: 3

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Linear algebra

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?