{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

AMS510HW1

# AMS510HW1 - AMS-510 Solution for HW1 September 9 2013...

This preview shows pages 1–4. Sign up to view the full content.

AMS-510 Solution for HW1 September 9 2013 Required Problems: 1.41, 1.45, 1,71 2.41, 2,55, 2,56, 2.69, 2.75, 2.79, 2.84, 2.85 3.53, 3.54 1.41 (a) 3 u - 2 v = 3(1 , - 2 , 4) - 2(3 , 5 , 1) = ( - 3 , - 16 , 10) (b) 5 u + 3 v - 4 w = 5(1 , - 2 , 4) + 3(3 , 5 , 1) - 4(2 , 1 , - 3) = (6 , 1 , 35) (c) u · v = (1 , - 2 , 4)(3 , 5 , 1) = 3 - 10 + 4 = - 3 u · w = (1 , - 2 , 4)(2 , 1 , - 3) = 2 - 2 - 12 = - 12 v · w = (3 , 5 , 1)(2 , 1 , - 3) = 6 + 5 - 3 = 8 1.45 (a) || u || = 1 + 4 + 16 = 21 || v || = 9 + 25 + 1 = 35 || w || = 4 + 1 + 9 = 14 1

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

View Full Document
(b) || k u || = 9 , || k || · || u || = 3 || u || = 3 · 1 + 4 + 4 = 9 || u+v || = 120 , || u || + || v || = 3 + 13 = 16 1.71 (a) ( u + v ) w = (( u 1 ,...,u n ) + ( v 1 ,...,v n )) · ( w 1 ,...w n ) = ( u 1 + v 1 n + v n ) · ( w 1 n ) = ( u 1 + v 1 ) + ... + ( u n + v n ) · w n = ( u 1 w 1 + ... + u n w n ) + ( v 1 w 1 + ... + v n w n ) = u · w + v · w (b) w ( u + v ) = ( w 1 n )(( u 1 n ) + ( v 1 n )) = ( w 1 n ) · ( u 1 + v 1 n + v n ) = w n · ( u 1 + v 1 ) + ... + ( u n + v n ) = ( w 1 u 1 + ... + w n u n ) + ( w 1 v 1 + ... + w n v n ) = w · u + w · v 2.41 (a) A T = ± 1 3 2 - 4 ² (b) B T = ± 5 - 6 0 7 ² (c) ( AB ) T = ± - 7 39 14 - 28 ² (d) A T B T = ± 5 15 10 - 40 ² 2
2.55 A - 1 = 1 1 2 1 2 5 1 3 7 - 1 = 1 1 1 2 - 5 3 - 1 2 - 1 B - 1 = 1 - 1 1 0 1 - 1 1 3 2 - 1 = 1 1 0 - 1 - 3 1 - 1 - 4 1 2.56 AB = AC A - 1 AB = A - 1 AC B = C A = ± 1 2 2 2 ² B = ± 0 0 1 1 ² C = ± 2 2 0 0 ² AB = ± 2 2 2 2 ² AC = ± 2 2 2 2 ² 2.69 (a) ( A + A T ) T = A T + ( A T ) T = A T + A (b) ( A - A T ) T = A T

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.

{[ snackBarMessage ]}

### Page1 / 6

AMS510HW1 - AMS-510 Solution for HW1 September 9 2013...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online