{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

20E_sheet1

# 20E_sheet1 - FACT SHEET FOR 20E EXAM 1 1 From Chapter 1 Dot...

This preview shows pages 1–2. Sign up to view the full content.

FACT SHEET FOR 20E EXAM 1 1. From Chapter 1 Dot product of two vectors v = ( v 1 , v 2 , . . . , v n ) and w = ( w 1 , w 2 , . . . , w n ): v · w = v 1 w 1 + v 2 w 2 + . . . + v n w n . Cross produce of two vectors in 3D (its a vector!): v × w = ( v 2 w 3 - v 3 w 2 , v 3 w 1 - v 1 w 3 , v 1 w 2 - v 2 w 1 ) . We have that v · ( v × w ) = w · ( v × w ) = 0 and the length v × w is the area of the parallelogram spanned by v and w . The direction obeys the “right hand rule”. The equation for a line through the vector x 0 and in the direction v 0 is ( t ) = x 0 + t v 0 . The matrix product of an n × m matrix ( a ij ) and an m × k matrix ( b ij ) is the n × k matrix ( c ij ) with c ij = m l =1 a il b lj . The determinant of a 2 × 2 matrix ( a ij ) is | A | = a 11 a 22 - a 12 a 21 . This is the area of the parallelogram spanned by the vectors ( a 11 , a 12 ) and ( a 21 , a 22 ). 2. From Chapter 2 The derivative matrix of the vector-valued function Φ : R n R k is the matrix D Φ | x 0 = ( j f i ( x 0 )), where the f i are the component functions of Φ .

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 / 2

20E_sheet1 - FACT SHEET FOR 20E EXAM 1 1 From Chapter 1 Dot...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online