If matrix A = begin{bmatrix} 1 & 3k + frac{1} | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let $A_k = \begin{bmatrix} 1 & 3k + \frac{1}{3} \ 0 & 1 \end{bmatrix}$.We know that $\begin{bmatrix} 1 & a \ 0 & 1 \end{bmatrix} \begin{bmatrix}

Vedclass · Accepted Answer

$\begin{bmatrix} 1 & 2010 \ 0 & 1 \end{bmatrix}$

Vedclass · Answer

(B) Let $A_k = \begin{bmatrix} 1 & 3k + \frac{1}{3} \ 0 & 1 \end{bmatrix}$.We know that $\begin{bmatrix} 1 & a \ 0 & 1 \end{bmatrix} \begin{bmatrix} 1 & b \ 0 & 1 \end{bmatrix} = \begin{bmatrix} 1 & a+b \ 0 & 1 \end{bmatrix}$.Therefore,the product $\prod_{k=1}^{36} A_k = \begin{bmatrix} 1 & \sum_{k=1}^{36} (3k + \frac{1}{3}) \ 0 & 1 \end{bmatrix}$.Calculate the sum: $\sum_{k=1}^{36} (3k + \frac{1}{3}) = 3 \sum_{k=1}^{36} k + \sum_{k=1}^{36} \frac{1}{3}$.$= 3 	imes \frac{36 	imes 37}{2} + 36 	imes \frac{1}{3}$.$= 3 	imes 18 	imes 37 + 12$.$= 54 	imes 37 + 12 = 1998 + 12 = 2010$.Thus,the product is $\begin{bmatrix} 1 & 2010 \ 0 & 1 \end{bmatrix}$.

If matrix $A = \begin{bmatrix} 1 & 3k + \frac{1}{3} \\ 0 & 1 \end{bmatrix}$,then the value of $\prod_{k=1}^{36} \begin{bmatrix} 1 & 3k + \frac{1}{3} \\ 0 & 1 \end{bmatrix}$ is equal to :-

Similar Questions

If $I$ is a unit matrix of order $10$,then the determinant of $I$ is equal to

If $A=\begin{bmatrix} 1 & 2 & -3 \\ 5 & 0 & 2 \\ 1 & -1 & 1 \end{bmatrix}$,$B=\begin{bmatrix} 3 & -1 & 2 \\ 4 & 2 & 5 \\ 2 & 0 & 3 \end{bmatrix}$,and $C=\begin{bmatrix} 4 & 1 & 2 \\ 0 & 3 & 2 \\ 1 & -2 & 3 \end{bmatrix}$,then compute $(A+B)$ and $(B-C)$. Also,verify that $A+(B-C)=(A+B)-C$.

If $A = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}$,then ${A^4} = $

If $A = \begin{bmatrix} 1 & a \\ 0 & 1 \end{bmatrix}$,then $A^4$ is equal to

If $A = \begin{bmatrix} 3 & 1 \\ -1 & 2 \end{bmatrix}$ and $A^2 - 5A = kI$,then $k =$ . . . . . .

Vedclass Test Series

Exam Paper Generator

Online Exam Module