Let `A` be an nth-order square matrix and `B` be its adjoint, then `|A B+K I_n|` is (where `K` is a scalar quantity) `(|A|+K)^(n-2)` b. `(|A|+)K^n` c.

Question

Let `A` be an nth-order square matrix and `B` be its adjoint, then `|A B+K I_n|` is (where `K` is a scalar quantity) `(|A|+K)^(n-2)` b. `(|A|+)K^n` c.

Let `A` be an nth-order square matrix and `B` be its adjoint, then `|A B+K I_n|` is (where `K` is a scalar quantity) `(|A|+K)^(n-2)` b. `(|A|+)K^n` c. `(|A|+K)^(n-1)` d. none of these
A. `(abs(A) +k)^(n-2) `
B. `(abs(A) +k)^(n)`
C. `(abs(A) +k)^(n-1)`
D. `(abs(A) +k)^(n+1)`

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
` because ` B = adj A
`rArr AB = A("ajd " A) = abs(A) I_(n)`
`therefore AB + KI_(n )= abs(A) I_(n) + kI_(n) = (abs(A) + k ) I_(n)`
`rArr abs( AB + KI_(n ))= abs((abs(A) + k))I_(n) = (abs(A) + k )^(n)`

4 views Answered 2023-02-05 15:29