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# 1 2 2 6 2 4 6 2 4 6 2 4 1 a a a a a b determinant is

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  1 2 2 6 2 4 6 2 4 6 2 4 1 a a a a a b) Determinant is not exist because it is not a square matrix.

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MATHEMATICS FOR MANAGEMENT BBMP1103 P a g e | 18 Prepared by Ezaidin bin Norman Tutor BBMP1103 T o p i c 1 M A T R I X 2.5 INVERSE MATRIX 1. Only for square matrices 2. Not all matrices have an inverse especially when the determinant 0 3. A matrix without an inverse is known as singular matrix 4. When a matrix is multiplied by its inverse 0 , the following properties are then true: a) I A A 1 b) I A A 1 5. The formula for deriving 1 A is as below, Adjoin A A 1 1 A Examples 2 11 4 0 1 0 2 15 6 2 1 1 A 1 2 11 2 0 2 1 0 1 2 15 3 I A A 1 0 0 0 1 0 0 0 1 1 2 11 2 0 2 1 0 1 2 15 3 3 3 2 0 2 0 1 4 1 1 I A A  1 0 0 0 1 0 0 0 1 3 3 2 0 2 0 1 4 1 1 2 11 2 0 2 1 0 1 2 15 3 1
MATHEMATICS FOR MANAGEMENT BBMP1103 P a g e | 19 Prepared by Ezaidin bin Norman Tutor BBMP1103 T o p i c 1 M A T R I X Exercise 2.4 (a) Find the inverse (if there exist any) for the following matrices. Then prove that your answers are correct. (i) 2 2 4 3 (ii) 1 2 1 1 0 0 4 3 2 (iii) 6 1 3 4 3 1 2 2 4 (iv) 3 2 1 2 3 2 1 4 1 (b) Given: 5 4 3 2 A (i) Find 1 A (ii) Show that A A 1 1 (c) Suppose: d c b a B (i) Determine 1 B (ii) State the properties required for the existence of 1 B (iii) Verify I B B BB 1 1

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MATHEMATICS FOR MANAGEMENT BBMP1103 P a g e | 20 Prepared by Ezaidin bin Norman Tutor BBMP1103 T o p i c 1 M A T R I X Solutions 2.4 (a) Find the inverse (if there exist any) for the following matrices. Then prove that your answers are correct. (i) 2 2 4 3 Step 1: Find the determinant A      14 8 6 2 4 2 3 Step 2: Find adjoin matrix 3 2 4 2 2 2 4 3 Step 3: Find inverse matrix Adjoin A 1 7 3 7 1 7 2 7 1 14 3 14 2 14 4 14 2 3 2 4 2 14 1 3 2 4 2 1 A (ii) 1 2 1 1 0 0 4 3 2 Step 1: Find the determinant A
MATHEMATICS FOR MANAGEMENT BBMP1103 P a g e | 21
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