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ArbitrLikvidat [17]
3 years ago
13

Prove the theorem (AB )^T= B^T. A^T

Mathematics
1 answer:
Lisa [10]3 years ago
3 0

Answer:

(AB)^T = B^T.A^T  (Proved)

Step-by-step explanation:

Given  (AB )^T= B^T. A^T;

To prove this expression, we need to apply multiplication law, power law and division law of indices respectively, as shown below.

(AB)^T = B^T.A^T\\\\Start, from \ Right \ hand \ side\\\\B^T.A^T = \frac{B^T.A^T}{A^T}.\frac{B^T.A^T}{B^T} (multiply \ through) \\\\                = \frac{A^{2T}.B^{2T}}{A^T.B^T} \\\\=\frac{(AB)^{2T}}{(AB)^T} \ \ (factor \ out \ the power)\\\\= (AB)^{2T-T}  \ (apply \ division \ law \ of \ indices; \ \frac{x^a}{x^b} = x^{a-b})\\\\= (AB)^T \ (Proved)

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\\ {\large{\textsf{\textbf{\underline{\underline{ Question \: :}}}}}}  \\

Factorise ;

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\qquad\rule{120pt}{2pt}

\\ {\large{\textsf{\textbf{\underline{\underline{ Solution \: :}}}}}}  \\

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\\\sf\implies\;{\underline{\boxed {\bf{ \:\:x=-6\:\: }}} }\red\bigstar \;\; \;\; \;{\underline{\boxed {\bf{ \:\:x=-1\:\: }}} }\red\bigstar \\

\\\qquad\rule{120pt}{2pt}\\

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</span>
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Andreyy89

Answer:

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Step-by-step explanation:

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