Let P be a matrix of order 3 × 3 such that all the entries in P are from the set - 1 ,   0,   1 . Then, the maximum possible value of the determinant of P is _______.

Question

Let P be a matrix of order 3 &#215; 3 such that all the entries in P are from the set - 1 , &#160; 0, &#160; 1 . Then, the maximum possible value of the determinant of P is _______.

Aicharya · Accepted Answer

&#8710; = a 1 a 2 a 3 b 1 b 2 b 3 c 1 c 2 c 3 = a 1 b 2 c 3 + a 2 b 3 c 1 + a 3 b 1 c 2 &#9183; x - a 3 b 2 c 1 + a 2 b 1 c 3 + a 1 b 3 c 2 &#9183; y Now if x &#8804; 3 and y &#8805; - 3 The &#8710; can be maximum 6 but it is not possible because x = 3 &#8658; each term of x = 1 And y = -3 &#8658; each term of y = - 1 &#8658; &#8719; i = 1 3 a i b i c i = 1 &#160; and &#8719; i = 1 3 a i b i c i = - 1 , which is a contradiction. Now for value to be 5 one the terms must be zero but that will make two terms zero which means answer cannot be 5 . Next possibility is 4 which can be obtained as 1 1 1 - 1 1 1 1 - 1 1 = 1 1 + 1 - 1 - 1 - 1 + 1 1 - 1 = 4

Let P be a matrix of order 3 × 3 such that all the entries in P are from the set - 1 ,   0,  …

Solution

Let P be a matrix of order 3 &#215; 3 such that all the entries in P are from the set - 1 , &#160; 0, &#160;…

Solution

Let P be a matrix of order 3 × 3 such that all the entries in P are from the set - 1 , 0, …