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Let A =\begin{bmatrix} 1 & 0& 0\\ 1& 1& 0\\ 1&1 &1 \end{bmatrix}  and B = A^{20} .  

Then the sum of the elements of the first column of B is :

  • Option 1)

    210

  • Option 2)

    211

  • Option 3)

    231

  • Option 4)

    251

 

Answers (1)

best_answer

As we have learned

Multiplication of matrices -

-

 

 A= \begin{bmatrix} 1 & 0&0 \\ 1& 1& 0\\ 1&1 & 1 \end{bmatrix}

A^{2}= \begin{bmatrix} 1 & 0&0 \\ 2& 1& 0\\ 3&2 & 1 \end{bmatrix}

 Thus  

A^{3}=\begin{bmatrix} 1 & -& -\\ 3& -&- \\ 6&- &- \end{bmatrix}

A^{20}=\begin{bmatrix} 1 & -& -\\ 20& -&- \\ 210&- &- \end{bmatrix}

sum of elements = 1+20+210= 231

 

 

 

 


Option 1)

210

This is incorrect

Option 2)

211

This is incorrect

Option 3)

231

This is correct

Option 4)

251

This is incorrect

Posted by

Himanshu

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