{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

math110s-hw5

math110s-hw5 - MATH 110 LINEAR ALGEBRA SPRING 2007/08...

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

View Full Document Right Arrow Icon

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

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

Unformatted text preview: MATH 110: LINEAR ALGEBRA SPRING 2007/08 PROBLEM SET 5 If T ¢ V V is a linear operator, we will write T n n times ³¹¹¹¹¹¹¹¹¹¹·¹¹¹¹¹¹¹¹¹¹µ T X X T , ie. T composed with itself n times. For example, T 2 T X T , T 3 T X T X T , etc. We will let O ¢ V W denote the zero linear transformation, ie. O v W for all v > V . The set of all linear transformations from V to W is denoted Hom F V,W . We write End F V for Hom F V,V . 1. Let U,W,V be finite-dimensional vector spaces over F . Let α,β > F . (a) Let T ¢ V W be a linear transformation. Show that rank T B dim V . (b) Let S ¢ U V and T ¢ V W be linear transformations. Show that rank T X S B rank T and rank T X S B rank S . (c) Let S 1 ¢ U V , S 2 ¢ U V , and T ¢ V W be linear transformations. Show that T X α S 1 β S 2 α T X S 1 β T X S 2 . (d) Let S ¢ U V , T 1 ¢ V W , and T 2 ¢ V W be linear transformations. Show that α T 1 β T 2 X S α T 1 X...
View Full Document

{[ snackBarMessage ]}

Page1 / 2

math110s-hw5 - MATH 110 LINEAR ALGEBRA SPRING 2007/08...

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

View Full Document Right Arrow Icon bookmark
Ask a homework question - tutors are online