tut2 - Math 235 Tutorial 2 Problems 1: Find a basis for the...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 235 Tutorial 2 Problems 1: Find a basis for the range and nullspace of the following linear mappings and verify the Rank-Nullity theorem. a) L : M 2 × 2 ( R ) P 2 , where L ±² a 11 a 12 a 21 a 22 ³´ = a 11 + ( a 12 + a 21 ) x + a 22 x 2 . b) L : M 2 × 3 ( R ) M 2 × 3 ( R ) where L ±² a b c d e f ³´ = ² d e f 0 0 0 ³ . 2: Find the matrix of each linear mapping with respect to the given bases B and C . a) L : P 2 R 2 defined by L ( ax 2 + bx + c ) = ² a + c b - a ³ , B = { x 2 + 1 ,x + 1 ,x 2 + x - 1 } , C = µ² 1 0 ³ , ² 1 1 ³¶ . b) Let U be the vector space of 2 × 2 upper triangular matrices.
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.
Ask a homework question - tutors are online