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UGC-NET | UGC-NET CS 2017 Dec 2 | Question 3

Last Updated : 15 Mar, 2018

54454

Find the boolean product A⊙B of the two matrices.
answer
(A) (1)
(B) (2)
(C) (3)
(D) (4)

Answer: (A)

Explanation: Here we have to follow two basics:
1- Matrics multiplication rule- For multiplication of two matrics, column in first matrics must be equal to rows in second matrics.
2- We have to find boolean product of two matrics so, we must know boolean product
ie
and table
No we have A=
$\begin{bmatrix} 1 &1 &0 \\ 0 & 1 & 0\\ 1 & 1 &0 \\ 0& 0 & 1 \end{bmatrix}$
and B=
$\begin{bmatrix} 1&0 &0 &0 \\ 0&1 &1 &0 \\ 1& 0 &1 &1 \end{bmatrix}$
Now the product AB=
$\begin{bmatrix} 1\cdot 1+ 1\cdot 0+0\cdot 1& 1\cdot 0 +1\cdot 1+0\cdot 0& 1\cdot 0+1\cdot 1+0\cdot 1 &1\cdot 0+1\cdot 0+0\cdot 1 \\ 0\cdot 1+1\cdot 0+0\cdot 1 &0\cdot 0+1\cdot 1+0\cdot 0 & 0\cdot0+1\cdot 1+0\cdot 1 &0\cdot 0+1\cdot 0+0\cdot 1\\ 1\cdot 1+1\cdot 0+0\cdot 1 & 1\cdot 0+1\cdot 1+0\cdot 0 &1\cdot 0+1\cdot 1+0\cdot 1 & 1\cdot 0+1\cdot 0+0\cdot 1\\ 0\cdot 1+0\cdot 0+1\cdot 1 &0\cdot 0+0\cdot 1+1\cdot 0 &0\cdot 0+0\cdot 1+1\cdot 1 & 0\cdot 0+0\cdot 0+1\cdot 1 \end{bmatrix}$
AB=
$\begin{bmatrix} 1 & 1&1 &0 \\ 0&1 & 1 & 0\\ 1 &1 & 1&0 \\ 1 &0 &1 &1 \end{bmatrix}$

So, option (A) is correct.

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