Assertion :If $D = d i a g [d_{1}, d_{2}, . . . ., d_{n}]$ , then $D^{- 1} = d i a g [d_{1}^{- 1}, d_{2}^{- 1} . . . . ., d_{n}^{- 1}]$ Reason: If $D = d i a g [d_{1}, d_{2}, . . . . . . d_{n}],$ then $D^{n} = d i a g [d_{1}^{n}, d_{2}^{n} . . . . . ., d_{n}^{n}] .$

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Assertion is incorrect but Reason is correct

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Solution

The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
$P r o p e r t y o f d i a g o n a l m a t r i x :$ If $D$ is a diagonal matrix, then $D^{n} = d i a g (d_{11}^{n}, d_{22}^{n}, . . . . . . . . . . . . . . . . . . ., d_{j j}^{n})$
Hence both $A$ and $R$ are correct but both are separate statements.
Hence both statements doesn't have mutual coordination.
Hence reason is not correct explanation of assertion.

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Similar questions

Q. If A is a diagonal matrix diag

(d_{1}, d_{2}, . . . . . . d_{n})

then

A^{n}, n ϵ R i s d i a g (d_{1}^{n}, d_{2}^{n} . . . . . d_{n}^{n})

Q. Assertion: The compressibility factor for

H_{2}

and

H e

(1 + \frac{P b}{R T})

Reason: The compressibility factor for

H_{2}

and

H e

can be derived from Van der Waal's equation.

Assertion (A) Order of the reaction can be zero or fractional.

Reason (R) We cannot determine order from balanced chemical equation.

(a) Both assertion and reason are correct and the reason is correct explanation of assertion
(b) Both assertion and reason are correct, but reason does not explain assertion.
(c) Assertion is correct, but reason is incorrect
(d) Both assertion and reason are incorrect
(e) Assertion is incorrect but reason is correct.

Assertion (A) Addition reaction of water to but-1-ene in acidic medium yields butan-1-ol.
Reason (R) Addition of water in acidic medium proceeds through the formation of primary carbocation.
(a) Assertion and reason both are correct and reason is correct explanation of assertion.
(b) Assertion and reason both are wrong statements.
(c) Assertion is correct statement but reason is wrong statement.
(d) Assertion is wrong statement but reason is correct statement.
(e) Both assertion and reason are correct statements but reason is not correct explanation of assertion.

Q. Assertion: Average kinetic energy in one oscillation during

SHM

of a body is

\frac{1}{4} m ω^{2} A^{2}

.
Reason: Maximum kinetic energy is

\frac{1}{2} m ω^{2} A^{2}

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Assertion :If D=diag[d1,d2,....,dn], then D−1=diag[d−11,d−12.....,d−1n] Reason: If D=diag[d1,d2,......dn], then Dn=diag[dn1,dn2......,dnn].

Assertion :If $D = d i a g [d_{1}, d_{2}, . . . ., d_{n}]$ , then $D^{- 1} = d i a g [d_{1}^{- 1}, d_{2}^{- 1} . . . . ., d_{n}^{- 1}]$ Reason: If $D = d i a g [d_{1}, d_{2}, . . . . . . d_{n}],$ then $D^{n} = d i a g [d_{1}^{n}, d_{2}^{n} . . . . . ., d_{n}^{n}] .$