





Last updated at Sept. 21, 2018 by Teachoo
Transcript
Example 29 The sum of three numbers is 6. If we multiply third number by 3 and add second number to it, we get 11. By adding first and third numbers, we get double of the second number. Represent it algebraically and find the numbers using matrix method. Let the first, second & third number be x, y, z respectively Given, x + y + z = 6 y + 3z = 11 x + z = 2y or x 2y + z = 0 Step 1 Write equation as AX = B 1 1 1 0 1 3 1 2 1 = 6 11 0 Hence A = 1 1 1 0 1 3 1 2 1 , X = & B = 6 11 0 Step 2 Calculate |A| = 1 1 1 0 1 3 1 2 1 = 1 (1 + 6) 0 (1 + 2) + 1 (3 1) = 7 + 2 = 9 So, |A| 0 The system of equation is consistent & has a unique solutions Now, AX = B X = A-1 B Hence A = 1 1 1 0 1 3 1 2 1 , X = & B = 6 11 0 = 1 (1 + 6) 0 (1 + 2) + 1 (3 1) = 7 + 2 = 9 0 Since determinant is not equal to O, A 1 exists Now find adj (A) adj (A) = 11 12 13 21 22 23 31 32 33 = 11 21 31 12 22 32 13 32 33 Now, AX = B X = A-1 B Step 3 Calculating X = A-1 B Calculating A-1 Now, A-1 = 1 |A| adj (A) adj A = A11 A12 A13 A21 A22 A23 A31 A32 A33 = A11 A21 A31 A12 A22 A32 A13 A23 A33 A = 1 1 2 3 4 5 2 1 3 11 = 1 1 3 ( 2) = 1 + 6 = 7 12 = 0 1 3 1 = ( 3) = 3 13 = 0 2 1 1= 1= 21 = 1 1 2 1 = 1+2 = 3 22 = 1 1 1 1 = 1 1 = 0 23 = 1 2 1 1 = 2 1 = 3 = 3 31 = 1 3 1 1 = 3 1 = 2 32 = 1 3 0 1 = 3 0 = 3 33 = 1 1 1 0 = 1 0 = 1 Hence, adj (A) = 7 3 2 3 0 3 1 3 1 Now, A 1 = 1 adj (A) A 1 = 1 9 7 3 2 3 0 3 1 3 1 Solution of given system of equations is X = A 1 B = 1 9 7 3 2 3 0 3 1 3 1 6 11 0 = 1 9 42 33+0 18+0+0 6+33+0 = 1 9 9 18 27 = 1 2 3 x = 1, y = 2, z = 3
Examples
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Example 8
Example 9
Example 10
Example 11
Example 12
Example 13
Example 14 Important
Example 15 Important
Example 16 Important
Example 17
Example 18 Important
Example 19
Example 20
Example 21
Example 22
Example 23
Example 24 Important
Example 25
Example 26 Important
Example 27
Example 28
Example 29 You are here
Example 30
Example 31
Example 32 Important
Example 33
Example 34 Important
About the Author