Matrices and Determinants 1 Question 6

6. Let P=[1004101641] and I be the identity matrix of order 3 . If Q=[qij] is a matrix, such that P50Q=I, then q31+q32q21 equals

(2016 Adv.)

(a) 52

(b) 103

(c) 201

(d) 205

Show Answer

Answer:

Correct Answer: 6. (b)

Solution:

  1. Here,

P=[1004101641]

P2=[1004101641][1004101641]=[1004+41016+324+41]=[1004×21016(1+2)4×21] and P3=[1004×21016(1+2)4×21][1004101641]=[1004×31016(1+2+3)4×31]

From symmetry,

P50=[1004×501016(1+2+3++50)4×501]P50Q=I [given] [1q11q12q13200q211q22q2316×502(51)q31200q321q33]=[100010001]200q21=0,16×50×512q31=0200q32=0q21=200,q32=200,q31=20400

 Thus, q31+q32q21=20400+200200=20600200=103



NCERT Chapter Video Solution

Dual Pane