Respostas

2013-11-13T15:28:32-02:00
Sabendo que A = | 1 0 0  |                    e B = | 2 0 0 |
                          | 0 -4 0 |                             | 0 4 0 |
                          | 0 0  3 |                             | x 0 2 |

A . B = 

ab11 = 1 * 2 + 0 * 0 + 0 * x = 2 + 0 + 0 = 2
ab12 = 1 * 0 +  0 * 4 +  0 * 0 = 0 + 0 + 0 = 0
ab13 = 1 * 0 +  0 * 0 +  0 * 2 = 0 + 0 + 0 = 0
ab21 = 0 * 2 + -4 * 0 +  0 * x = 0 + 0 + 0 = 0
ab22 = 0 * 0 +  -4 * 4 +  0 * 0 = -16
ab23 = 0 * 0 + -4 *0 +  0 * 2 = 0
ab31 = 0 * 2 + 0 * 0 +  3 * x = 3x
ab32 = 
0 * 0 + 0 * 4 + 3 * 0 = 0
ab33 = 
0 * 0 + 0 * 0 +  3 * 2 = 6

ba11 = 2 * 1 +  0 * 0 +  0* 0 = 2
ba12 = 2 *  0 + 0 * - 4 +  0* 0 = 0
ba13 = 2 *0+  0 * 0+0*3=0
ba21 = 0 * 1 + 4 * 0 +  0 *  0 = 0
ba22 = 0 * 0 + 4 *-4 +  0 * 0 = -16
ba23 = 0 * 0 + 4 * 0 + 0 * 3 =0 
ba31 = x * 1 + 0 * 0 + 2 * 0 = 1x 
ba32 = x * 0 + 0 * -4 + 0 * 0 = 0
ba33 = x * 0 + 0 * 0 + 2 * 3 = 6




A . B                                  B.A
2     0  0                             2  0  0 
0  -16  0                             0  -16  0
3x  0   6                             1x  0   6

Resposta: Para que A . B seja igual B . A, x deve assumir o valor de Raíz quadrada de 3.