Tarea de Mate (matrices) ejercicios 20-29.docx

Tarea de Mate (matrices) ejercicios 20-29.docx - 3 B= A=...

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20. Si A = ( 5 67 ) , B = ( 3 4 1 ) y C = ( 1 2 4 0 1 1 3 2 1 ) , encuentre: a) AB, b) BA, c) (BA)C, d) (AB)C. Solución: a) AB A = ( 5 67 ) B = ( 3 4 1 ) ¿ ( 5 ) ( 3 ) + ( 6 ) ( 4 ) + ( 7 ) ¿ 15 24 7 = ( 16 ) b) BA B = ( 3 4 1 ) A = ( 5 67 ) ¿ ( ( 3 ) ( 5 ) ( 3 ) ( 6 ) ( 3 ) ( 7 ) ( 4 ) ( 5 ) ( 4 ) [ 6 ] ( 4 ) ( 7 ) ( 1 ) ( 5 ) ( 1 ) ( 6 ) ( 1 ) ( 7 ) ) = ( 15 18 21 20 24 28 5 6 7 ) c) (BA)C A = ( 5 67 ) B = ( 3 4 1 ) C = ( 1 2 4 0 1 1 3 2 1 ) ¿ ( 15 18 21 20 24 28 5 6 7 )( 1 2 4 0 1 1 3 2 1 )
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¿ ( ( 15 ) ( 1 ) + ( 18 ) ( 0 ) + ( 21 ) ( 3 ) ( 15 ) ( 2 ) + ( 18 ) ( 1 ) + ( 21 ) ( 2 ) ( 15 ) ( 4 ) + ( 18 ) ( 1 ) + ( 21 ) ( 1 ) ( 20 ) ( 1 ) + ( 24 ) ( 0 ) + ( 28 ) ( 3 ) ( 20 ) ( 2 ) + ( 24 ) ( 1 ) + ( 28 ) ( 2 ) ( 20 ) ( 4 ) + ( 24 ) ( 1 ) + ( 28 ) ( 1 ) ( 5 ) ( 1 ) + ( 6 ) ( 0 ) + ( 7 ) ( 3 ) ( 5 ) ( 2 ) + ( 6 ) ( 1 ) + ( 7 ) ( 2 ) ( 5 ) ( 4 ) + ( 6 ) ( 1 ) + ( 7 ) ( 1 ) ) ¿ ( ( 15 + 0 + 63 ) ( 30 18 + 42 ) ( 60 + 18 + 21 ) ( 20 + 0 + 84 ) ( 40 24 + 56 ) ( 80 + 24 + 28 ) ( 5 + 0 21 ) ( 10 + 6 14 ) ( 20 6 7 ) ) = ( 78 54 99 104 72 132 26 18 33 ) d) (AB)C AB es una matriz de 1x1 y C es una matriz de 3x3, por lo tanto las matrices no se pueden operar. 21. Si A = ( 4 8 10 ) y B = ( 245 ) , encuentre: a) A T A , b) B T B , c) A + B T Solución: a) A T A A = ( 4 8 10 ) ¿ ( 4 8 10 ) ( 4 8 10 ) = ( 4 ) ( 4 ) + ( 8 ) ( 8 ) + ( 10 ) ( 10 ) = ( 16 + 64 + 100 ) = ( 180 ) b) B T B ¿ ( 2 4 5 ) ( 245 )
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( ( 2 ) ( 2 ) ( 2 ) ( 4 ) ( 2 ) ( 5 ) ( 4 ) ( 2 ) ( 4 ) ( 4 ) ( 4 ) ( 5 ) ( 5 ) ( 2 ) ( 5 ) ( 4 ) ( 5 ) ( 5 ) ) = ( 4 8 10 8 16 20 10 20 25 ) c) A + B T A = ( 4 8
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  • Spring '17
  • david
  • A=, B T B

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