Question

यदि $A= \begin{bmatrix} 1 & 0 & 1 \\ 0 & 1 & 2 \\ 0 & 0 & 4 \end{bmatrix}$ हो तो दिखाइए कि |3A| = 27|A|

Answer 1

Answer:

3 a =3xयदि [tex] A= \begin{bmatrix} 1 & 0 & 1 \\ 0 & 1 & 2 \\ 0 & 0 & 4 \

and 4a = 4 x यदि [tex] A= \begin{bmatrix} 1 & 0 & 1 \\ 0 & 1 & 2 \\ 0 & 0 & 4 \

Answer 2

Given :   $A= \begin{bmatrix} 1 & 0 & 1 \\ 0 & 1 & 2 \\ 0 & 0 & 4 \end{bmatrix}$

To find :  दिखाइए कि |3A| = 27|A|

Solution :

$A= \begin{bmatrix} 1 & 0 & 1 \\ 0 & 1 & 2 \\ 0 & 0 & 4 \end{bmatrix}$     =>       $3A= \begin{bmatrix} 3 & 0 & 3 \\ 0 & 3 & 6 \\ 0 & 0 & 12 \end{bmatrix}$

$A= \begin{bmatrix} 1 & 0 & 1 \\ 0 & 1 & 2 \\ 0 & 0 & 4 \end{bmatrix}$

Det A = | A |  =  1 ( 1 * 4 - 0 * 2)  - 0 ( 0 * 4 - 0 * 2)  + 1 ( 0 * 0  - 0 * 1)

| A | = 4 - 0  - 0

| A | = 4

$3A= \begin{bmatrix} 3 & 0 & 3 \\ 0 & 3 & 6 \\ 0 & 0 & 12 \end{bmatrix}$

Det3A = | 3A |   = 3 ( 3 * 12 - 0 * 6)  - 0 ( 0 * 12 - 0 * 6)  + 3 ( 0 * 0  - 0 * 3)

| 3A | = 108  - 0 - 0

| 3A |  =  108

=> | 3A |  = 27 (4)

=> |3A |  =  27 |A|

QED

इति  सिद्धम

और सीखें

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