Awesome q2a theme
0 votes
12 views

Number of $n$x$n$ matrices that can be constructed with $m$ different matrix elements

According to me it should be $m^{n*n}$. Is it correct?


and the follow up question with this concept in use

All elements of a $2$x$2$ matrix "A" can have values either $0$ or $1$. The probability that any element gets a value $(0$ or $1)$ is $1/2$. If all elements of this matrix are chosen at random, what is the probability that the determinant of this matrix is positive?

My answer to the above problem is → $3/16$


Please verify both

ago in Calculus by (613 points) | 12 views
0
0
First one seems right.

Second one:

How can you make a 0/1 matrix of order 2 negative ? By ensuring the determinant evaluates as $0 - 1 = -1$

i.e. The leading diagonal has to multiply to 0, and other diagonal has to multiple to 1.
Therefore, the leading diagonal can be (0,0), (0,1),(1,0) and the other diagonal is (1,1).

So I think out of 16 possible combinations, 3 combinations will yield a negative determinant:

$\begin{bmatrix} 0&1 \\ 1&0 \end{bmatrix}$, $\begin{bmatrix} 0&1 \\ 1&1 \end{bmatrix}$, $\begin{bmatrix} 1&1 \\ 1&0 \end{bmatrix}$.

Probability of a negative determinant $= \frac{3}{16}$

Probability of a positive determinant $= 1- \frac{3}{16} = \frac{13}{16}$

What is the right answer ?

Edit: my definition of positive is 'non-negative', so I've included $0$ too
0
0 is neither positive nor negative right?
0
Ya that is why u got 13/16

or else it should have been 3/16 i guess

Btw 0 is neither positive nor negative right?
+1
I knew that'd be a question. That is why with matrices, you'd use the term non-singular instead. Or non-zero positive in case of integers. Or natural numbers.

But yes, you're right.
0
Okay..

Thanks.. :)

Please log in or register to answer this question.

Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true
Welcome to GATE CSE Doubts, where you can ask questions and receive answers from other members of the community.
Top Users Jan 2020
  1. shashin

    1163 Points

  2. Vimal Patel

    306 Points

  3. Deepakk Poonia (Dee)

    305 Points

  4. Debapaul

    237 Points

  5. Satbir

    192 Points

  6. SuvasishDutta

    137 Points

  7. Pratyush Priyam Kuan

    118 Points

  8. tp21

    108 Points

  9. DukeThunders

    96 Points

  10. pranay562

    95 Points

Monthly Top User and those within 60% of his/her points will get a share of monthly revenue of GO subject to a minimum payout of Rs. 500. Current monthly budget for Top Users is Rs. 75.
2,989 questions
1,509 answers
8,935 comments
89,814 users