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Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Transcript

Example 16 Solve the system of equations 2x + 5y = 1 3x + 2y = 7 Step 1 Write equation as AX = B [โ– 8(2&5@3&2)] [โ– 8(๐‘ฅ@๐‘ฆ)] = [โ– 8(1@7)] A = [โ– 8(2&5@3&2)] , X = [โ– 8(๐‘ฅ@๐‘ฆ)] , B = [โ– 8(1@7)] Step 2 Calculate |A|, A = [โ– 8(2&5@3&2)] |A| = |โ– 8(2&5@3&2)| = 2 ร— 2 โ€“ 5 ร— 3 = 4 โ€“ 15 = โ€“ 11 Since |๐‘จ| โ‰  0, System is consistent and the system of equations has a unique solution AX = B X = A-1 B Step 3 Calculating X = A-1 B Here, A-1 = 1/(|A|) adj (A) adj A = [โ– 8(2&5@3&2)] = [โ– 8(2&โˆ’5@โˆ’3&2)] Now, A-1 = 1/(|A|) adj A Putting values = ๐Ÿ/(โˆ’๐Ÿ๐Ÿ) [โ– 8(๐Ÿ&โˆ’๐Ÿ“@โˆ’๐Ÿ‘&๐Ÿ)] & B = [โ– 8(1@7)] Now X = A-1 B [โ– 8(๐‘ฅ@๐‘ฆ)] = (โˆ’1)/11 [โ– 8(2&โˆ’5@โˆ’3&2)] [โ– 8(1@7)] [โ– 8(๐‘ฅ@๐‘ฆ)] = (โˆ’1)/11 [โ– 8(2(1)+(โคถ7โˆ’5)7@โˆ’3(1)+2(7))] [โ– 8(๐‘ฅ@๐‘ฆ)] = (โˆ’1)/11 [โ– 8(2โˆ’35@โˆ’3+14)] = (โˆ’1)/11 [โ– 8(โˆ’33@11)] = [โ– 8(โˆ’33 ร— (โˆ’1)/11@11 ร— (โˆ’1)/11)] [โ– 8(๐‘ฅ@๐‘ฆ)] = [โ– 8(3@โˆ’1)] Hence x = 3 & y = โ€“ 1

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.