**Ex 4.6, 15**

Last updated at March 11, 2017 by Teachoo

Last updated at March 11, 2017 by Teachoo

Transcript

Ex4.6, 15 If A = 2−3532−411−2, find A−1. Using A−1 solve the system of equations 2x – 3y + 5z = 11 3x + 2y – 4z = -5 x + y – 2z = -3 Step 1 Write equation as AX = B 2−3532−411−2 𝑥𝑦𝑧 = 11−5−3 i.e. AX = B Hence A = 2−3532−411−2 , X = 𝑥𝑦𝑧 & B = 11−5−3 Step 2 Calculate |A| |A|= 2−3532−411−2 = 2 (−4 + 4) − 3 (6 − 5) + 1 (12 − 10) = 2(0) − 3 (1) + 1(2) = −1 So, |A|≠ 0 ∴ The system of equation is consistent & has a unique solutions 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 = −4 + 4 = 0 𝐴12 = − −6−(−4) = − (−6 + 4) = −2 = 2 𝐴13 = 3 − 2 = 1 𝐴21 = (6 − 5) = −1 𝐴22 = −4 − 5 = −9 𝐴23 = −2−(−3 = −5 𝐴31 = 12−10=2 𝐴32 = −8−15=23 𝐴33 = 4− −9=13 Thus adj A = 0−122−9231−513 & |A| = –1 Now, A-1 = 1|A| adj A A-1 = 1−1 0−122−9231−513 = 01−2−29−23−15−13 Solving X = A-1 B 𝑥𝑦𝑧 = − 01−229−23−15−13 11−5−3 𝑥𝑦𝑧 = −5+6−22−45+69−11−25+39 𝑥𝑦𝑧 = 123 ∴ x = 1, y = 2 and z = 3

Ex 4.1, 7
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Example 14 Important

Example 15 Important

Example 16 Important

Ex 4.2, 7 Important

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Ex 4.2, 11 Important

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Example 18 Important

Ex 4.3, 2 Important

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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 You are here

Ex 4.6, 16 Important

Example 32 Important

Example 34 Important

Misc. 2 Important

Misc 11 Important

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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

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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.