1
Question
Find 12(A+AT) and 12(A−AT), when A=⎡⎢⎣0−a−ba0−cbc0⎤⎥⎦
Open in App
Solution
A=⎡⎢⎣0−a−ba0−cbc0⎤⎥⎦
The given matrix is
A=⎡⎢⎣0−a−ba0−cbc0⎤⎥⎦
∴AT=⎡⎢⎣0ab−a0c−b−c0⎤⎥⎦
A+AT=⎡⎢⎣0−a−ba0−cbc0⎤⎥⎦+⎡⎢⎣0ab−a0c−b−c0⎤⎥⎦=⎡⎢⎣000000000⎤⎥⎦
∴12(A+AT)=⎡⎢⎣000000000⎤⎥⎦
Now, A−AT=⎡⎢⎣0−a−ba0−cbc0⎤⎥⎦−⎡⎢⎣0ab−a0c−b−c0⎤⎥⎦=⎡⎢⎣0−2a−2b2a0−2c2b2c0⎤⎥⎦
∴12(A−AT)=⎡⎢⎣0−a−ba0−cb0⎤⎥⎦
The given matrix is
A=⎡⎢⎣0−a−ba0−cbc0⎤⎥⎦
∴AT=⎡⎢⎣0ab−a0c−b−c0⎤⎥⎦
A+AT=⎡⎢⎣0−a−ba0−cbc0⎤⎥⎦+⎡⎢⎣0ab−a0c−b−c0⎤⎥⎦=⎡⎢⎣000000000⎤⎥⎦
∴12(A+AT)=⎡⎢⎣000000000⎤⎥⎦
Now, A−AT=⎡⎢⎣0−a−ba0−cbc0⎤⎥⎦−⎡⎢⎣0ab−a0c−b−c0⎤⎥⎦=⎡⎢⎣0−2a−2b2a0−2c2b2c0⎤⎥⎦
∴12(A−AT)=⎡⎢⎣0−a−ba0−cb0⎤⎥⎦
Suggest Corrections
0
Similar questions
View More
Join BYJU'S Learning Program
Explore more
Join BYJU'S Learning Program
