{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

081st_tut1sol

# 081st_tut1sol - MATH1111/2008-09/Tutorial I Solution 1...

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: MATH1111/2008-09/Tutorial I Solution 1 Tutorial I Suggested Solution 1. Let a 1 = ï£« ï£­ 1- 2- 5 ï£¶ ï£¸ , a 2 = ï£« ï£­ 2 5 6 ï£¶ ï£¸ , b = ï£« ï£­ 7 4- 3 ï£¶ ï£¸ . Determine whether b is a linear combination of a 1 and a 2 . Give it a geometrical interpretation. Ans . Want to find scalars Î± and Î² so that Î± a 1 + Î² a 2 = b . In other words, Î± ï£« ï£­ 1- 2- 5 ï£¶ ï£¸ + Î² ï£« ï£­ 2 5 6 ï£¶ ï£¸ = ï£« ï£­ 7 4- 3 ï£¶ ï£¸ . It can be expressed as a system of linear equation ï£± ï£² ï£³ Î± + 2 Î² = 7- 2 Î± + 5 Î² = 4- 5 Î± + 6 Î² =- 3 Its augmented matrix is ï£« ï£­ 1 2 7- 2 5 4- 5 6- 3 ï£¶ ï£¸ which reduces via elementary row operations to ï£« ï£­ 1 0 3 0 1 2 0 0 ï£¶ ï£¸ i.e. Î± = 3 and Î² = 2, or b = 3 a 1 + 2 a 2 is a linear combination of a i , i = 1 , 2. View a i as vectors (arrows) in R 3 , the sum of them after a suitable scaling yields the vector b . MATH1111/2008-09/Tutorial I Solution 2 2. Let A be a nonsingular matrix. Show that A T is also nonsingular and find the inverse of A T ....
View Full Document

{[ snackBarMessage ]}

### Page1 / 4

081st_tut1sol - MATH1111/2008-09/Tutorial I Solution 1...

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

View Full Document
Ask a homework question - tutors are online