Let `f(x)=(1+x)/(1-x)` . If `A` is matrix for which `A^3=O ,t h e nf(A)` is `I+A+A^2` b. `I+2A+2A^2` c. `I-A-A^2` d. none of these

Question

Let `f(x)=(1+x)/(1-x)` . If `A` is matrix for which `A^3=O ,t h e nf(A)` is `I+A+A^2` b. `I+2A+2A^2` c. `I-A-A^2` d. none of these

Let `f(x)=(1+x)/(1-x)` . If `A` is matrix for which `A^3=O ,t h e nf(A)` is `I+A+A^2` b. `I+2A+2A^2` c. `I-A-A^2` d. none of these
A. `I+A+A^(2)`
B. `I+2A+2A^(2)`
C. `I-A-A^(2)`
D. none of these

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - B
`(I-A) f(A)=I+A`
or `f(A)=(I+A)(I-A)^(-1)`
`=(I+A)(I+A+A^(2))`
`=I+A+A^(2)+A+A^(2)+A^(3)`
`=I+2A+2A^(2)`

4 views Answered 2023-02-05 15:29