Question

A=((1&2@1&3)),B=(4&0@1&5)),C= ((2&0@1&2)) எனில் கீழ்கண்டவற்றை நிருபி
(A-B)C=AC-BC

Answer 1

Answer:

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Answer 2

விளக்குக:

$A=\left[\begin{array}{ll}1 & 2 \\1 & 3\end{array}\right]$

$B=\left[\begin{array}{ll}4 & 0 \\1 & 5\end{array}\right]$

$C=\left[\begin{array}{ll}2 & 0 \\1 & 2\end{array}\right]$

(A-B)C=AC-BC

இடப்பக்கம்

(A-B)C

$A-B=\left[\begin{array}{ll}1 & 2 \\1 & 3\end{array}\right]-\left[\begin{array}{ll}4 & 0 \\1 & 5\end{array}\right]$

          $=\left[\begin{array}{ll}1-4 & 2-0 \\1-1 & 3-5\end{array}\right]$

           $=\left[\begin{array}{cc}-3 & 2 \\0 & -2\end{array}\right]$

$(A-B) C=\left[\begin{array}{cc}-3 & 2 \\0 & -2\end{array}\right]\left[\begin{array}{ll}4 & 0 \\1 & 5\end{array}\right]$

               $=\left[\begin{array}{cc}-6+2 & 0+4 \\0-2 & 0-4\end{array}\right]$

               $=\left[\begin{array}{cc}-4 & 4 \\-2 & -4\end{array}\right]$........(1)

வலப்பக்கம்

AC-BC

$A C=\left[\begin{array}{ll}1 & 2 \\1 & 3\end{array}\right]\left[\begin{array}{ll}2 & 0 \\1 & 2\end{array}\right]$

      $=\left[\begin{array}{ll}2+2 & 0+4 \\2+3 & 0+6\end{array}\right]=\left[\begin{array}{ll}4 & 4 \\5 & 6\end{array}\right]$

$B C=\left[\begin{array}{ll}4 & 0 \\1 & 5\end{array}\right]\left[\begin{array}{ll}2 & 0 \\1 & 2\end{array}\right]$

      $=\left[\begin{array}{cc}8+0 & 0+0 \\2+5 & 0+10\end{array}\right]$

       $=\left[\begin{array}{cc}8 & 0 \\7 & 10\end{array}\right]$

$A C-B C =$ $\left[\begin{array}{ll}4 & 4 \\2 & 4\end{array}\right]-\left[\begin{array}{ll}8 & 0 \\7 & 10\end{array}\right]$

                = $\left[\begin{array}{cc}4-8 & 4-0 \\5-7 & 6-10\end{array}\right]$

$AC - BC = \left[\begin{array}{cc}-4 & 4 \\-2 & -4\end{array}\right]$...........(2)

(1),(2)லிருந்து

இடப்பக்கம் = வலப்பக்கம்

A-B)C=AC-BC என நிரூபிக்கப்பட்டது.