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Suma y Resta de Matrices

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Suma y Resta de Matrices

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Operaciones entre matrices

Created by

AP Education
AP Education
Peru

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Suma y Resta de Matrices
 

Suma y Resta de MatricesOnline version

Operaciones entre matrices

by AP Education
1

1) ¿Qué condiciones deben cumplir dos matrices para poder sumarlas?

2

2) Suma A=[[1,2],[3,4]] y B=[[5,6],[7,8]]. ¿Cuál es el resultado A+B?

3

3) Si A es 2×3 y B es 2×3, ¿cuál de estas es una entrada válida de A−B en la posición (1,2)?

4

4) ¿Qué pasa si intentas sumar A de 2×2 y B de 3×2?

5

5) Si A=[[0,−1],[2,3]] y B=[[1,4],[−2,0]], ¿A+B en (2,1)?

6

6) ¿Qué nota diferencia hay entre suma y resta de matrices?

7

7) Dada A=[[2,0],[5,1]] y B=[[−2,4],[3,−1]], ¿A−B en (1,2)?

8

8) ¿Qué resultado tiene A+B si A=[[1,1],[1,1]] y B=[[1,−1],[−1,1]]?

9

9) ¿Cuál es la suma de matrices identidad I2 y −I2 (2×2)?

10

10) En términos prácticos, ¿para qué sirve sumar matrices en álgebra lineal?

Explicación

La suma solo es posible si ambas matrices son de la misma forma, es decir, m×n.

Suma elemento a elemento: 1+5=6, 2+6=8, etc.

La resta se realiza elemento a elemento en la misma posición.

Las dimensiones deben coincidir exactamente; de lo contrario, no es válida.

Elemento (2,1) es A(2,1)=2 y B(2,1)=−2; suma es 0.

Resta equivale a sumar con la matriz opuesta.

En (1,2) A=0, B=4; 0−4=−4.

Suma elemento a elemento: 1+1=2, 1+(−1)=0, etc.

I2−I2 da la matriz nula.

La suma de matrices ayuda a combinar vectores, coeficientes y sistemas lineales.

 
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