The correct option is C I + B^T From equation ⇒ ( A+AB )^T ⇒ A^T+B^TA^T { We known that ( AB )^T=B^TA^T} ⇒ A^T ( ...

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Standard XII

Mathematics

Transpose of a Matrix

A+ABT=XAT, ...

Question

$(A + A B)^{T} = X A^{T}$ , $X =$

B^{T}

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B

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I

+

B^{T}

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B^{T} A^{T}

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Solution

The correct option is C $I$ $+$ $B^{T}$
From equation
$\Rightarrow {(A + A B)}^{T}$
$\Rightarrow A^{T} + B^{T} A^{T}$ ${W e k n o w n t h a t {(A B)}^{T} = B^{T} A^{T}}$
$\Rightarrow A^{T} (I + B^{T})$
$\Rightarrow A^{T} X$
$∴$ $X = I$ $+$ $B^{T}$

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(A+AB)T=XAT, X=

The correct option is C I + BTFrom equation ⇒(A+AB)T⇒AT+BTAT {Weknownthat(AB)T=BTAT}⇒AT(I+BT)⇒ATX∴ X=I + BT

$(A + A B)^{T} = X A^{T}$ , $X =$

The correct option is C $I$ $+$ $B^{T}$
From equation
$\Rightarrow {(A + A B)}^{T}$
$\Rightarrow A^{T} + B^{T} A^{T}$ ${W e k n o w n t h a t {(A B)}^{T} = B^{T} A^{T}}$
$\Rightarrow A^{T} (I + B^{T})$
$\Rightarrow A^{T} X$
$∴$ $X = I$ $+$ $B^{T}$