Chapter 3 Class 12 Matrices
Ex 3.1, 9 (MCQ) Important
Example 18 Important
Example 19
Ex 3.2, 7 (i)
Ex 3.2, 12 Important
Ex 3.2, 16 Important You are here
Ex 3.2, 17 Important
Ex 3.2, 20 Important
Example 22 Important
Ex 3.3, 4 Important
Ex 3.3, 10 (i) Important
Ex 3.3, 12 (MCQ)
Question 15 Important Deleted for CBSE Board 2024 Exams
Question 17 Important Deleted for CBSE Board 2024 Exams
Example 25
Question 3 Important Deleted for CBSE Board 2024 Exams
Misc 6 Important
Misc 8 Important
Misc 9 (MCQ)
Chapter 3 Class 12 Matrices
Last updated at April 16, 2024 by Teachoo
Ex 3.2, 16 If A = [■8(1&0&2@0&2&1@2&0&3)] , prove that A3 – 6A2 + 7A + 2I = O Finding A2 A2 = A × A = [■8(1&0&2@0&2&1@2&0&3)] [■8(1&0&2@0&2&1@2&0&3)] = [■8(1(1)+0 (0)+2(2)&1(0)+0(2)+2(0)&1(2)+0(1)+2(3)@0(1)+2(0)+1(2)&0(0)+2(2)+1(0)&0(2)+2(1)+1(3)@2(1)+0(0)+3(2)&2(0)+0(2)+3(0)&2(2)+0(1)+3(3))] = [■8(1+0+4&0+0+0&2+0+6@0+0+2&0+4+0&0+2+3@2+0+6&0+0+0&4+0+9)] = [■8(𝟓&𝟎&𝟖@𝟐&𝟒&𝟓@𝟖&𝟎&𝟏𝟑)] Finding A3 A3 = A2. A = [■8(5&0&8@2&4&5@8&0&13)] [■8(1&0&2@0&2&1@2&0&3)] = [■8(5(1)+0 (0)+8(2)&5(0)+0(2)+8(0)&5(2)+0(1)+8(3)@2(1)+4(0)+5(2)&2(0)+4(2)+5(0)&2(2)+4(1)+5(3)@8(1)+0(0)+13(2)&8(0)+0(2)+13(0)&8(2)+0(1)+13(3))] = [■8(5+0+16&0+0+0&10+0+24@2+0+10&0+8+0&4+4+15@8+0+26&0+0+0&16+0+39)] = [■8(𝟐𝟏&𝟎&𝟑𝟒@𝟏𝟐&𝟖&𝟐𝟑@𝟑𝟒&𝟎&𝟓𝟓)] Now calculating A3 - 6A2 +7A + 2I Putting values = [■8(21&0&34@12&8&23@34&0&55)] – 6 [■8(5&0&8@2&4&5@8&0&13)] + 7 [■8(1&0&2@0&2&1@2&0&3)] + 2 [■8(1&0&0@0&1&0@0&0&1)] = [■8(21&0&34@12&8&23@34&0&55)] – [■8(6(5)&0(5)&8(6)@2(6)&4(6)&5(6)@8(6)&0(6)&13(6))] + [■8(1(7)&0(7)&2(7)@0(7)&2(7)&1(7)@2(7)&0(7)&3(7))] + [■8(2(1)&2(0)&2(0)@2(0)&1(2)&0(2)@2(0)&0(2)&1(2))] = [■8(21−30+7+2&0−0+0+0&34−48+14+0@12−12+0+0&8−24+14+2&23−30+7+0@34−48+14+0&0+0+0+0&55−78+21+2)] = [■8(−30+30&0&−48+48@12−12&24−24&30−30@48−48&0&78−78)] = [■8(𝟎&𝟎&𝟎@𝟎&𝟎&𝟎@𝟎&𝟎&𝟎)] = O Thus, A3 – 6A2 + 7A + 2I = O Hence proved