1KOI REPLY TO KARO YAAR
let A be the set of all 3X3 determinant having entries +1 or -1. if a determinant D from set A is chosen randomly, then probability that product of elemrnts of any row or any column is -1 is
a) 1/32 b) 1/8 c)1/16 d) none
ans a)1/32
nt getting ans pls help
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25 Answers
1meself getting above 250
quite a number of my frnds above 250....one getting 400 even
wat abt u ????????/
1HOW MANY MARKS U ASPECT TO GET IN THIS FIITJEE FULL TEST 12
I WILL GET AROUND 250
1\begin{bmatrix} -1 & -1 &-1 \\ -1& 1 & 1\\ -1& 1&1 \end{bmatrix}\begin{bmatrix} -1 & -1 &-1 \\ 1& -1 & 1\\ 1& - 1&1 \end{bmatrix}\begin{bmatrix} -1 & -1 &-1 \\ 1& 1 & -1\\ 1& 1&-1 \end{bmatrix}\begin{bmatrix} -1 & 1 &1 \\ -1& -1 & -1\\ -1& 1&1 \end{bmatrix}\begin{bmatrix} 1 & -1 &1 \\ -1& -1 &- 1\\ 1& - 1&1 \end{bmatrix}\begin{bmatrix} 1 & 1 &-1 \\ -1& -1 &- 1\\ 1& 1&-1 \end{bmatrix}\begin{bmatrix} 1 & 1 &-1 \\ 1& 1 &- 1\\ - 1& - 1&-1 \end{bmatrix}\begin{bmatrix} -1 &1 &1 \\ - 1& 1 &1\\ - 1& - 1&-1 \end{bmatrix}}\begin{bmatrix} 1 &- 1 &1 \\ 1& -1 &1\\ - 1& - 1&-1 \end{bmatrix}
1me too missed the last 9 cases.......
they proceeded like tis total 9 positions...two choices
hence 2^9
1@uttara
at last got 16 cases
first 2 as harsh showed 1+6=7
then consider the fourth case as harsh showed
1 full row n 1 full column
we get 8
the last one is all the edges -1
hence 16
latex not working[2]
1\begin{bmatrix} -1 & -1 &- 1 \\ -1& -1 &-1 \\ -1 & -1 & -1 \end{bmatrix}
\begin{bmatrix} -1 & 1 & 1 \\ 1&- 1 &1 \\ 1 & 1 &- 1 \end{bmatrix}\begin{bmatrix} 1 & -1 & 1 \\ 1& 1 &-1 \\ -1 & 1 & 1 \end{bmatrix}\begin{bmatrix} 1 & 1 & -1 \\ - 1& 1 &1 \\ 1 &- 1 & 1 \end{bmatrix}\begin{bmatrix} -1 & 1 & 1 \\ 1& 1 &-1 \\ 1 &- 1 & 1 \end{bmatrix}\begin{bmatrix} 1 & -1 & 1 \\ - 1& 1 &1 \\ 1 & 1 & -1 \end{bmatrix}\begin{bmatrix} 1 & 1 & -1 \\ 1&- 1 &1 \\ -1 & 1 & 1 \end{bmatrix}
1boss first atleast show 9 different cases.....we are not getting more than 7..
saare cases wit diagram n explanation pls
1THE ANSWER OF PROBABILITY SHOULD BE GREATER THAN 1/32
BECAUSE THERE ARE MORE THAN 16 CASES
1FOR FIRST DIAGRAM ONLY 1
FOR SECOND DIAGRAM :- SELECT 1 NEGATIVE IN FIRST ROW THEN THERE ARE 2 PLACES FOR SECOND NEGATIVE AND AFTER PLACING 2ND THERE IS ONLY 1 PLACE FOR 3RD NEGATIVE SO 3x2x1=6 CASES
FOR 3 DIAGRAM : PLEASE CHECK YOURSELF[1]
4I considered 1st one of ur matrices as one case and 2nd as 3! cases
that is 1 + 6 = 7 cases in total
ur 3rd is also included in these 3! cases
1SEE IN THESE EXAMPLES THAT MULTIPLICATION OF ANY ROW OR COLUMN IS -1 AND THERE IS 16 MATRICES THAT FORMED LIKE THIS
1SEE EXAMPLES OF CASES LIKE
\begin{bmatrix} -1 & -1 & -1\\ -1& -1 &-1 \\ -1& -1 & -1 \end{bmatrix}ONLY 1 LIKE THIS
\begin{bmatrix} -1 & 1 & 1\\ 1& -1 &1 \\ 1& 1 & -1 \end{bmatrix} ONLY 6 LIKE THIS
\begin{bmatrix} -1 & -1 & -1\\ 1 & 1 &-1 \\ 1& 1 & -1 \end{bmatrix} 9 LIKE THIS
4@Harsh : u speaking abt all possible total no of dets or cases where product of elements is ±1???
1I THINK THEY SOLVED THE PROBLEM BY SUPPOSING THAT PRODUCT OF ENTRIES OF EACH INDIVIDUAL ROW AND COLUMN IS -1
1sir in q it is given determinant......
but in the soln they took total cases as 2^9 ??[12]
cud u please provide solution for both the cases......
341Please clarify whether its a matrix or a determinant. Because for a determinant a matrix and its transpose will not be distinct elements of the set A.