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Example 3 Important
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Example 5 Important
Example 6
Example 7
Example 8
Example 9
Example 10
Example 11 Important
Example 12
Example 13 Important
Example 14
Example 15
Example 16 Important
Example 17
Example 18 Important You are here
Example 19
Example 20 Important
Example 21
Example 22 Important
Example 23 Deleted for CBSE Board 2022 Exams
Example 24 Important Deleted for CBSE Board 2022 Exams
Example 25 Important Deleted for CBSE Board 2022 Exams
Example 26 Important
Example 27 Important
Example 28
Last updated at Jan. 17, 2020 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.