Question

evaluate:
265 240 219
240 225 198
219 198 181

matrices??

Answer 1

Given :   matrix  $\begin {bmatrix} {265 & 240 & 219 \\ 240 & 225 & 198 \\ 219 & 198 & 181 } \end{bmatrix}$

To find  :  Evaluate

Solution:

$\begin {bmatrix} {265 & 240 & 219 \\ 240 & 225 & 198 \\ 219 & 198 & 181 } \end{bmatrix}$

R₁ → R₁ - R₂

= $\begin {bmatrix} {25 & 15 & 21 \\ 240 & 225 & 198 \\ 219 & 198 & 181 } \end{bmatrix}$

R₂ → R₂ - R₃

= $\begin {bmatrix} {25 & 15 & 21 \\ 21 & 27 & 17 \\ 219 & 198 & 181 } \end{bmatrix}$

R₁ → R₁ - R₂

= $\begin {bmatrix} {4 & -12 & 4 \\ 21 & 27 & 17 \\ 219 & 198 & 181 } \end{bmatrix}$

C₁ → C₁ - C₃

=  $\begin {bmatrix} {0 & -12 & 4 \\ 4 & 27 & 17 \\ 38 & 198 & 181 } \end{bmatrix}$

C₂ → C₂ + 3C₃

= $\begin {bmatrix} {0 & 0 & 4 \\ 4 & 78 & 17 \\ 38 & 741 & 181 } \end{bmatrix}$

C₂ → C₂/39

= $\begin {bmatrix} {0 & 0 & 4 \\ 4 & 2 & 17 \\ 38 & 19 & 181 } \end{bmatrix}$

C₁ → C₁/2

= $\begin {bmatrix} {0 & 0 & 4 \\ 2 & 2 & 17 \\19 & 19 & 181 } \end{bmatrix}$

C₁ → C₁ - C₂

= $\begin {bmatrix} {0 & 0 & 4 \\ 0 & 2 & 17 \\0 & 19 & 181 } \end{bmatrix}$

= 0

other method :

$\begin {bmatrix} {265 & 240 & 219 \\ 240 & 225 & 198 \\ 219 & 198 & 181 } \end{bmatrix}$

= 265 ( 225 * 181  - 198 * 198) - 240(240 * 181 - 219 * 198) + 219(240*198 - 219 * 225)

= 265 ( 1521) - 240(78)  + 219(-1755)

= 18720 - 18720

= 0

Learn more:

निम्नलिखित सारणिकों के मान ज्ञात कीजिए

(i)  -3 & -1 & 2  \\  0 & 0 & -1 \\ 3 & -5 & 0  

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