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  • Let A be  matrix having entries from the set <img alt="\{-1,0,1\}" src="https://entrancecor

Let A be 3\times 3 matrix having entries from the set \{-1,0,1\}. The number of all such matrices A having sum of all the entries equal to 5, is____________.

Option: 1

414


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

\mathrm{Given \: matrix\: 3\times 3= \begin{bmatrix} - & - &- \\ -& -& -\\ -& - & - \end{bmatrix} }
Here we can see we have to find nine elements whose sum is 5.

Case-1 when five 1's  are there & four 0's are there.
Again by division & distribution method
\mathrm{\text { we \, get } \Rightarrow \frac{9 !}{5 ! 4 !}=126 \cdots \cdots \text { (i) }}

Case-2 when six 1's  are there & one \left \{ -1 \right \} & two 0's are there.
Again by division & distribution method
\mathrm{\text { we get } \Rightarrow \frac{9 !}{6 ! 2 ! 1 !}=252 \cdots \cdots (i i)}

Case-3 when seven 1's  are there are two \left \{ -1 \right \} are there,
 By division & distribution we get
\mathrm{\Rightarrow \frac{9 !}{7 ! 2 !}=36 \cdots\cdots \text { (iii) }}

Now adding eqn (i)+(ii)+(iii)

\text{we get}\: 126+252+36= 414
So total 414 ways will be there.

Posted by

Shailly goel

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