4.3 Properties of Determinants 1

# 4.3 Properties of Determinants 1 - 4.3 4.3 Properties of...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 4.3. 4.3. Properties of Determinants 1. (a) F (p.223) (b) T (Theorem 4.7 p. 223) (c) F (d) T (e) F (Theorem 4.8 p. 224) (f) T (g) F (h) F 2. (a) A = a 11 a 12 a 21 a 22 ¶ and b = b 1 b 2 ¶ Since det( A ) = a 11 a 22- a 12 a 21 6 = 0, Cramer’s rule applies Using the notation of theorem 4.9, we have x 1 = det( M 1 ) / det( A ) = ( b 1 a 22- a 12 b 2 ) / ( a 11 a 22- a 12 a 21 ) x 2 = det( M 2 ) / det( A ) = ( b 2 a 11- a 21 b 1 ) / ( a 11 a 22- a 12 a 21 ) ∴ x = ( x 1 ,x 2 ) = (( b 1 a 22- a 12 b 2 ) / ( a 11 a 22- a 12 a 21 ) , ( b 2 a 11- a 21 b 1 ) / ( a 11 a 22- a 12 a 21 )) 3. 198 PNU-MATH 4.3. A = 2 1- 3 1- 2 1 3 4- 2 , b = 5 10 , det( A ) =- 25 det( M 1 ) = det 5 1- 3 10- 2 1 4- 2 , det( M 2 ) = det 2 5- 3 1 10 1 3- 2 , det( M 3 ) = det 2 1 5 1- 2 10 3 4 x 1 = det( M 1 ) / det( A ) =- 100 /- 25 = 4 x 2 = det( M 2 ) / det( A ) = 75 /- 25 =- 3 x 3 = det( M 3 ) / det( A ) = 0 /- 25 = 0 ∴ x = (4 ,- 3 , 0) 5. (4 ,- 3 , 0) 7. (0 ,- 12 , 16) 8....
View Full Document

{[ snackBarMessage ]}

### Page1 / 7

4.3 Properties of Determinants 1 - 4.3 4.3 Properties of...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online