AIEEE was so simple

Algebra Level 4

How many 3 × 3 3 \times 3 non-singular matrices exist with four entries as 1 1 and all other entries as 0 0 ?

(Source - AIEEE 2010)
At least 7 At most 4 6 5

Akhil Bansal by Akhil Bansal , 22, India

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3 solutions

Otto Bretscher
Sep 6, 2015

There are n ! ( n − 1 ) n = 36 n!(n-1)n=36 such matrices. Take any of the six 3 × 3 3\times3 permutation matrices, and replace any of the 6 zeroes in such a matrix by a 1.

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Aaryan Vaishya
Nov 10, 2018

All you really need to do is find 7 matrices with 4 ones.

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Ramiel To-ong
Sep 11, 2015

AT LEAST SEVEN FOR THE MINIMUM IS SEVEN

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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