Let A = 2 - 2 1 - 1 and B = - 1 2 - 1 2 . Then the number of elements in the set n , m : n , m ∈ 1 , 2 , … … . 10 and n A n + m B m = I is _____.

Question

Let A = 2 - 2 1 - 1 and B = - 1 2 - 1 2 . Then the number of elements in the set n , m : n , m &#8712; 1 , 2 , &#8230; &#8230; . 10 and n A n + m B m = I is _____.

Quantrex Academy · Accepted Answer

Correct answer: 0

Given, A = 2 - 2 1 - 1 So, A 2 = 2 - 2 1 - 1 2 - 2 1 - 1 = 2 - 2 1 - 1 = A Also, B = - 1 2 - 1 2 B 2 = - 1 2 - 1 2 - 1 2 - 1 2 = - 1 2 - 1 2 = B So, A + B = 2 - 2 1 - 1 + - 1 2 - 1 2 = 1 0 0 1 = I Therefore the equation n A n + m B m = I is true for n = 1 &#160; &#38; &#160; m = 1 so, only one set is possible.

Let A = 2 - 2 1 - 1 and B = - 1 2 - 1 2 . Then the number of elements in the set n , m : n , m ∈ 1 , 2 , … … . 10 and n A n + m B m = I is _____.

Correct answer

Step-by-step solution

More from Matrices

Let A = 2 - 2 1 - 1 and B = - 1 2 - 1 2 . Then the number of elements in the set n , m : n , m &#8712; 1 , 2 , &#8230; &#8230; . 10 and n A n + m B m = I is _____.

Correct answer

Step-by-step solution

More from Matrices

Let A = 2 - 2 1 - 1 and B = - 1 2 - 1 2 . Then the number of elements in the set n , m : n , m ∈ 1 , 2 , … … . 10 and n A n + m B m = I is _____.