# Ex 4.6, 16

Last updated at March 11, 2017 by Teachoo

Last updated at March 11, 2017 by Teachoo

Transcript

Ex 4.6, 16 The cost of 4 kg onion, 3 kg wheat and 2 kg rice is Rs 60. The cost of 2 kg onion, 4 kg wheat and 6 kg rice is Rs 90. The cost of 6 kg onion 2 kg wheat and 3 kg rice is Rs 70. Find cost of each item per kg by matrix method Let the cost of onion, wheat & rice per kg be x, y, z respectively. Given, Cost of 4kg onion, 3 kg wheat & 2 kg rice is Rs 60. 4x + 3y + 2z = 60 Cost of 2kg onion, 4kg wheat & 6kg rice is Rs 90. 2x + 4y + 6z = 90 Cost of 6kg onion, 2kg wheat & 3 kg Rice is Rs 70 6x + 2y + 3z = 70 So the system of equation is 4x + 3y + 2z = 60 x + 2y + 3z = 45 6x + 2y + 3z = 70 Step 1 Write equation as AX = B 432123623 𝑥𝑦𝑧 = 604570 Hence A = 432123623, X = 𝑥𝑦𝑧 & B = 604570 Step 2 Calculate |A| 𝐴 = 432123623 = 4 (6 − 6) − 1(9 − 4) + 6 (9 − 4) = 4 (0) − 1 (5) + 6 (5) = − 5 + 30 = 25 So, |A|≠ 0 ∴ The system of equation is consistent & has a unique solutions 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 = A11A12A13A21A22A23A31A32A33′ = A11A21A31A12A22A32A13A23A33 A = 1−1234−52−13 𝐴11 = 2 × 3 − 2 × 3 = 6 − 6 = 0 𝐴12 = − 3×1−6×3 = − 3−18 = − (−15) = 15 𝐴22 = 4 × 3 − 6 × 2 = 12 − 12 = 0 𝐴23 = − 2×1−6×2 = − 2−12 = − (−10) = 10 𝐴31 = 3 × 3 − 2 × 2 = 9 − 4 = 5 𝐴32 = − 4×3−2×1 = 12−2=−10 𝐴33 = 4 × 2 − 3 × 1 = 8 − 3 = 5 Hence, adj (A) = 0−55150−10−10105 Now, A−1 = 1 𝐴 adj (A) A−1 = 125 0−55150−10−10105 = 15 0−1130−2−221 Now, X = A−1 B 𝑥𝑦𝑧 = 15 − 0−1130−2−221 604570 𝑥𝑦𝑧 = 15 −0−45+70180+0−140−120+90+70 = 15 254040 𝑥𝑦𝑧 = 588 ∴ x = 5, y = 8, z = 8 Cost of onion, wheat & rice per kg is Rs 5, Rs 8 & Rs 8 Respectively.

Ex 4.1, 7
Important

Example 14 Important

Example 15 Important

Example 16 Important

Ex 4.2, 7 Important

Ex 4.2, 8 Important

Ex 4.2, 11 Important

Ex 4.2, 12 Important

Ex 4.2, 13 Important

Ex 4.2, 14 Important

Ex 4.2, 15 Important

Example 18 Important

Ex 4.3, 2 Important

Ex 4.3, 3 Important

Example 24 Important

Example 26 Important

Ex 4.5, 10 Important

Ex 4.5, 15 Important

Ex 4.5, 18 Important

Ex 4.6, 13 Important

Ex 4.6, 15 Important

Ex 4.6, 16 Important You are here

Example 32 Important

Example 34 Important

Misc. 2 Important

Misc 11 Important

Misc. 15 Important

Misc. 16 Important

Misc. 19 Important

Important Question for exams Class 12

- Chapter 1 Class 12 Relation and Functions
- Chapter 2 Class 12 Inverse Trigonometric Functions
- Chapter 3 Class 12 Matrices
- Chapter 4 Class 12 Determinants
- Chapter 5 Class 12 Continuity and Differentiability
- Chapter 6 Class 12 Application of Derivatives
- Chapter 7 Class 12 Integrals
- Chapter 8 Class 12 Application of Integrals
- Chapter 9 Class 12 Differential Equations
- Chapter 10 Class 12 Vector Algebra
- Chapter 11 Class 12 Three Dimensional Geometry
- Chapter 12 Class 12 Linear Programming
- Chapter 13 Class 12 Probability

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.