JEE Main202427 Jan 2024Morning ShiftMathematicsMatricesActual
Let A = 2 0 1 1 1 0 1 0 1 , B = B 1 B 2 B 3 , where B 1 , B 2 , B 3 are column matrices, and AB 1 = 1 0 0 , AB 2 = 2 3 0 , AB 3 = 3 2 1 If α = | B | and β is the sum of all the diagonal elements of B , then α 3 + β 3 is equal to
Correct answer
0
Step-by-step solution
Given: A = 2 0 1 1 1 0 1 0 1 , B = B 1 B 2 B 3 , B 1 = x 1 y 1 z 1 , B 2 = x 2 y 2 z 2 and B 3 = x 3 y 3 z 3 . ⇒ AB 1 = 2 0 1 1 1 0 1 0 1 x 1 y 1 z 1 = 1 0 0 ⇒ 2 x 1 + 0 + z 1 x 1 + y 1 + 0 x 1 + 0 + z 1 = 1 0 0 ⇒ 2 x 1 + z 1 = 1 , x 1 + y 1 = 0 , x 1 + z 1 = 0 ⇒ x 1 = 1 , y 1 = - 1 , z 1 = - 1 ⇒ AB 2 = 2 0 1 1 1 0 1 0 1 x 2 y 2 z 2 = 2 3 0 ⇒ AB 2 = 2 x 2 + z 2 x 2 + y 2 x 2 + z 2 = 2 3 0 ⇒ 2 x 2 + z 2 = 2 , x 2 + y 2 = 3 , x 2 + z 2 = 0 ⇒ x 2 = 2 , y 2 = 1 , z 2 = - 2 ⇒ AB 3 = 2 0 1 1 1 0 1 0 1 x 3 y 3 z 3 = 3 2 1