Lect23 - Chapter 4. Linear Transformations Math1111 Matrix...

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Chapter 4. Linear Transformations Math1111 Matrix Representations Theorem 4.2.2 - Remarks (Cont’d) Example . Let w 1 = ( - 2 1 ) T , w 2 = ( 3 2 - 1 2 ) T be a basis for R 2 . Find the matrix representation of the identity map Id : R 2 R 2 r.t. E = [ e 1 , e 2 ] and F = [ w 1 , w 2 ] .
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Chapter 4. Linear Transformations Math1111 Matrix Representations Theorem 4.2.2 - Remarks (Cont’d) Example . Let w 1 = ( - 2 1 ) T , w 2 = ( 3 2 - 1 2 ) T be a basis for R 2 . Find the matrix representation of the identity map Id : R 2 R 2 r.t. E = [ e 1 , e 2 ] and F = [ w 1 , w 2 ] . Ans . Evaluate [ Id ( e i )] F ( i = 1,2 ) .
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Chapter 4. Linear Transformations Math1111 Matrix Representations Theorem 4.2.2 - Remarks (Cont’d) Example . Let w 1 = ( - 2 1 ) T , w 2 = ( 3 2 - 1 2 ) T be a basis for R 2 . Find the matrix representation of the identity map Id : R 2 R 2 r.t. E = [ e 1 , e 2 ] and F = [ w 1 , w 2 ] . Ans . Evaluate [ Id ( e i )] F ( i = 1,2 ) . We get 1 3 2 4
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Chapter 4. Linear Transformations Math1111 Matrix Representations Theorem 4.2.2 - Remarks (Cont’d) Example . Let w 1 = ( - 2 1 ) T , w 2 = ( 3 2 - 1 2 ) T be a basis for R 2 . Find the matrix representation of the identity map Id : R 2 R 2 r.t. E = [ e 1 , e 2 ] and F = [ w 1 , w 2 ] . Ans . Evaluate [ Id ( e i )] F ( i = 1,2 ) . We get 1 3 2 4 Example . Let dim V = 2 , E = [ v 1 , v 2 ] , F = [ w 1 , w 2 ] be ordered bases for V where v 1 = w 1 + 2 w 2 , v 2 = 3 w 1 + 4 w 2 . Find the matrix representation of the identity map Id : V V r.t. E and F .
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Chapter 4. Linear Transformations Math1111 Matrix Representations Theorem 4.2.2 - Remarks (Cont’d) Example . Let w 1 = ( - 2 1 ) T , w 2 = ( 3 2 - 1 2 ) T be a basis for R 2 . Find the matrix representation of the identity map Id : R 2 R 2 r.t. E = [ e 1 , e 2 ] and F = [ w 1 , w 2 ] . Ans . Evaluate [ Id ( e i )] F ( i = 1,2 ) . We get 1 3 2 4 Example . Let dim V = 2 , E = [ v 1 , v 2 ] , F = [ w 1 , w 2 ] be ordered bases for V where v 1 = w 1 + 2 w 2 , v 2 = 3 w 1 + 4 w 2 . Find the matrix representation of the identity map Id : V V r.t. E and F . Ans . Evaluate [ Id ( v i )] F ( i = ) .
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Chapter 4. Linear Transformations Math1111 Matrix Representations Theorem 4.2.2 - Remarks (Cont’d) Example . Let w 1 = ( - 2 1 ) T , w 2 = ( 3 2 - 1 2 ) T be a basis for R 2 . Find the matrix representation of the identity map Id : R 2 R 2 r.t.
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This note was uploaded on 04/30/2010 for the course MATH 1111 taught by Professor Dr,li during the Spring '10 term at HKU.

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Lect23 - Chapter 4. Linear Transformations Math1111 Matrix...

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