CBSE Class 12 Sample Paper for 2026 Boards
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CBSE Class 12 Sample Paper for 2026 Boards
Last updated at Sept. 2, 2025 by Teachoo
This question is similar to Chapter 4 Class 12 Determinants - Examples
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Transcript
Question 32 For two matrices ๐ด=[โ (3&โ6&โ1@2&โ5&โ1@โ2&4&1)] and ๐ต=[โ (1&โ2&โ1@0&โ1&โ1@2&0&3)], find the product ๐ด๐ต and hence solve the system of equations: 3๐ฅโ6๐ฆโ๐ง=3 2๐ฅโ5๐ฆโ๐ง+2=0 โ2๐ฅ+4๐ฆ+๐ง=5Finding the product AB = [โ (3&โ6&โ1@2&โ5&โ1@โ2&4&1)] [โ (1&โ2&โ1@0&โ1&โ1@2&0&3)] =[โ 8(3(1)+(โคถ7โ6)(0)+(โ1)(2)&3(โ2)+(โ6)(โ1)+(โ1)(0)&3(โ1)+(โ6)(โ1)+(โ1)(3)@2(1)+(โ5)(0)+(โ1)(2)&2(โ2)+(โ5)(โ1)+(โ1)(0)&2(โ1)+(โ5)(โ1)+(โ1)(3)@(โ2)(1)+4(0)+1(2)&(โ2)(โ2)+4(โ1)+1(0)&(โ2)(โ1)+4(โ1)+1(3))] = [โ 8(1@0@0)" " โ 8(0@1@0)" " โ 8(0@0@1)] Thus, AB = I We know that AA-1 = I So ๐ฉ is inverse of A Now, solving the equation Given equations are 3๐ฅโ6๐ฆโ๐ง=3 2๐ฅโ5๐ฆโ๐ง=โ2 โ2๐ฅ+4๐ฆ+๐ง=5 Writing the equation as AX = D [โ (3&โ6&โ1@2&โ5&โ1@โ2&4&1)][โ 8(๐ฅ@๐ฆ@๐ง)] = [โ 8(3@โ2@5)] Here A =[โ (3&โ6&โ1@2&โ5&โ1@โ2&4&1)], X = [โ 8(๐ฅ@๐ฆ@๐ง)] & D = [โ 8(3@โ2@5)] Now, AX = D X = A-1 D Putting A-1 = ๐ฉ=[โ (1&โ2&โ1@0&โ1&โ1@2&0&3)] So, our equation becomes [โ 8(๐ฅ@๐ฆ@๐ง)] =[โ (1&โ2&โ1@0&โ1&โ1@2&0&3)][โ 8(3@โ2@5)] [โ 8(๐ฅ@๐ฆ@๐ง)] = [โ 8(1(3)+(โคถ7โ2)(โ2)+(โ1) (5)@0(3)+(โ1)(โ2)+(โ1)(5)@2(3)+0(โ2)+3(5))] [โ 8(๐ฅ@๐ฆ@๐ง)] = [โ 8(3+4โ5@0+2โ5@6+0+15)] [โ 8(๐ฅ@๐ฆ@๐ง)] = [โ 8(2@โ3@21)] Hence x = 2 , y = โ3 & z = 21
