Question

hlo guys answere this plzz..
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Answer 1

Answer:

(iv) is right answer. please brain list me

Answer 2

Question :

1) $\left[\begin{array}{c c c}2 & 1 & 3\end{array}\right] + \left[\begin{array}{c c c}0 & 0 & 0\end{array}\right]$

2) $\left[\begin{array}{c c c}0 \\ 1 \\ -1\end{array}\right] + \left[\begin{array}{c c c}-1 \\ 1 \\ 0\end{array}\right]$

3) $\left[\begin{array}{c c c}3 & 9 & 0 \\ 1 & 8 & -2\end{array}\right] + \left[\begin{array}{c c c}4 & 0 & 2 \\ 7 & 1 & 4\end{array}\right]$

4) $\left[\begin{array}{c c c}-1 & 2 \\ 1 & -2 \\ 3 & -1\end{array}\right] + \left[\begin{array}{c c c}0 & 1 \\ -1 & 0 \\ -2 & 1\end{array}\right]$

Concept :

We know that :

$:\implies \left[\begin{array}{c c c}x & y & z \\ y & x & z \\ z & y & x \end{array}\right] + \left[\begin{array}{c c c}z & y & x \\ y & x & z \\ x & y & z \end{array}\right]$

$:\implies \left[\begin{array}{c c c}x + z & y + y & z + x \\ y + y & x + x & z + z \\ z + x & y + y & x + z\end{array}\right]$

$\therefore \left[\begin{array}{c c c}x & y & z \\ y & x & z \\ z & y & x \end{array}\right] + \left[\begin{array}{c c c}z & y & x \\ y & x & z \\ x & y & z \end{array}\right] = \left[\begin{array}{c c c}x + z & y + y & z + x \\ y + y & x + x & z + z \\ z + x & y + y & x + z\end{array}\right]$

So by using the above information in the below Questions , we can find the required value.

Solution.i :

$\left[\begin{array}{c c c}2 & 1 & 3\end{array}\right] + \left[\begin{array}{c c c}0 & 0 & 0\end{array}\right]$

$:\implies \left[\begin{array}{c c c}2 & 1 & 3\end{array}\right] + \left[\begin{array}{c c c}0 & 0 & 0\end{array}\right]$

$:\implies \left[\begin{array}{c c c}2 + 0 & 1 + 0 & 3 + 0 \end{array}\right]$

$:\implies \left[\begin{array}{c c c}2 & 1 & 3\end{array}\right]$

$\therefore \left[\begin{array}{c c c}2 & 1 & 3\end{array}\right] + \left[\begin{array}{c c c}0 & 0 & 0\end{array}\right] = \left[\begin{array}{c c c}2 & 1 & 3\end{array}\right]$

Solution.ii :

$:\implies \left[\begin{array}{c c c}0 \\ 1 \\ -1\end{array}\right] + \left[\begin{array}{c c c}-1 \\ 1 \\ 0\end{array}\right]$

$:\implies \left[\begin{array}{c c c}0 + (-1) \\ 1 + 1 \\ -1 + 0\end{array}\right]$

$:\implies \left[\begin{array}{c c c}-1 \\ 2 \\ -1\end{array}\right]$

$\therefore \left[\begin{array}{c c c}0 \\ 1 \\ -1\end{array}\right] + \left[\begin{array}{c c c}-1 \\ 1 \\ 0\end{array}\right] = \left[\begin{array}{c c c}-1 \\ 2 \\ -1\end{array}\right]$

Solution.iii :

$:\implies \left[\begin{array}{c c c}3 & 9 & 0 \\ 1 & 8 & -2\end{array}\right] + \left[\begin{array}{c c c}4 & 0 & 2 \\ 7 & 1 & 4\end{array}\right]$

$:\implies \left[\begin{array}{c c c}3 + 4 & 9 + 0 & 0 + 2 \\ 1 + 7 & 8 + 1 & -2 + 4\end{array}\right]$

$:\implies \left[\begin{array}{c c c}7 & 9 & 2 \\ 8 & 9 & 2\end{array}\right]$

$\therefore \left[\begin{array}{c c c}3 & 9 & 0 \\ 1 & 8 & -2\end{array}\right] + \left[\begin{array}{c c c}4 & 0 & 2 \\ 7 & 1 & 4\end{array}\right] = \left[\begin{array}{c c c}7 & 9 & 2 \\ 8 & 9 & 2\end{array}\right]$

Solution.iv :

$:\implies \left[\begin{array}{c c c}-1 & 2 \\ 1 & -2 \\ 3 & -1\end{array}\right] + \left[\begin{array}{c c c}0 & 1 \\ -1 & 0 \\ -2 & 1\end{array}\right]$

$:\implies \left[\begin{array}{c c c}-1 + 0 & 2 + 1 \\ 1 + (-1) & -2 + 0 \\ 3 + (-2) & -1 + 1\end{array}\right]$

$:\implies \left[\begin{array}{c c c}-1 & 3 \\ 0 & -2 \\ 1 & 0\end{array}\right]$

$\therefore \left[\begin{array}{c c c}-1 & 2 \\ 1 & -2 \\ 3 & -1\end{array}\right] + \left[\begin{array}{c c c}0 & 1 \\ -1 & 0 \\ -2 & 1\end{array}\right] = \left[\begin{array}{c c c}-1 & 3 \\ 0 & -2 \\ 1 & 0\end{array}\right]$

$\rule{400}{2}$