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Chapter 3 Class 12 Matrices
Ex 3.1, 9 (MCQ) Important
Example 18 Important You are here
Example 19
Ex 3.2, 7 (i)
Ex 3.2, 12 Important
Ex 3.2, 16 Important
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 June 8, 2023 by Teachoo
Example 18 If A = [■8(1&2&3@3&−2&1@4&2&1)] then show that A3 – 23A – 40I = O Finding A2 A2 = AA = [■8(1&2&3@3&−2&1@4&2&1)] [■8(1&2&3@3&−2&1@4&2&1)] = [■8(1(1)+2(3)+3(4)&1(2)+2(−2)+3(2)&1(3)+2(1)+3(1)@3(1)+(−2)(3)+1(4)&3(2)+(−2)(−2)+1(2)&3(3)+(−2)(1)+1(1)@4(1)+2(3)+1(4)&4(2)+2(−2)+1(2)&4(3)+(2)(1)+1(1))] = [■8(1+6+12&2−4+6&3+2+3@3−6+4&6+4+2&9−2+1@4+6+4&8−4+2&12+2+1)] = [■8(𝟏𝟗&𝟒&𝟖@𝟏&𝟏𝟐&𝟖@𝟏𝟒&𝟔&𝟏𝟓)] Finding A3 A3 = A2 A = [■8(19&4&8@1&12&8@14&6&15)] [■8(1&2&3@3&−2&1@4&2&1)] = [■8(19(1)+4(3)+8(4)&19(2)+4(−2)+8(2)&19(3)+4(1)+8(1)@1(1)+12(3)+8(4)&1(2)+12(−2)+8(2)&1(3)+12(1)+8(1)@14(1)+6(3)+15(4)&14(2)+6(−2)+15(2)&14(3)+6(1)+15 (1))] = [■8(19+12+32&38−8+16&57+4+8@1+36+32&2−24+16&3+12+8@14+18+60&28−12+30&42+6+15)] = [■8(𝟔𝟑&𝟒𝟔&𝟔𝟗@𝟔𝟗&−𝟔&𝟐𝟑@𝟗𝟐&𝟒𝟔&𝟔𝟑)] Calculating A3 – 23A – 40I = [■8(63&46&69@69&−6&23@92&46&63)] −23 [■8(1&2&3@3&−2&1@4&2&1)] −40 [■8(1&0&0@0&1&0@0&0&1)] = [■8(63&46&69@69&−6&23@92&46&63)] −[■8(23×1&23×2&23×3@23×3&23×(−2)&23×1@23×4&23×(2)&23×1)] − [■8(1×40&0×40&0×40@0×40&1×40&0×40@0×40&0×40&1×40)] = [■8(63&46&69@69&−6&23@92&46&63)] ⤶7− [■8(23&46&69@69&−46&23@92&46&23)] ⤶7− [■8(40&0&0@0&40&0@0&0&40)] = [■8(63−23−40&46−46+0&69−69+0@69−69+0&−6+46−40&23−23+0@92−92+0&46−46+0&63−23−40)] = [■8(𝟎&𝟎&𝟎@𝟎&𝟎&𝟎@𝟎&𝟎&𝟎)] = O Hence proved.