If the product of n matrices $$110112011301$$.......$$.1n01$$ is equal to the matrix $$137801$$, the value of n is equal to

$$110112011301$$.......$$.1n01=1n(n+1)201=137801$$ ⇒$$n(n+1)2=378$$⇒$$n=27$$

Operations of matrix

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If the product of n matrices $[\begin{matrix} 1 & 1 \\ 0 & 1 \end{matrix}] [\begin{matrix} 1 & 2 \\ 0 & 1 \end{matrix}] [\begin{matrix} 1 & 3 \\ 0 & 1 \end{matrix}] . . . . . . . . [\begin{matrix} 1 & n \\ 0 & 1 \end{matrix}]$ is equal to the matrix $[\begin{matrix} 1 & 378 \\ 0 & 1 \end{matrix}]$ , the value of n is equal to

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Solution

$[\begin{matrix} 1 & 1 \\ 0 & 1 \end{matrix}] [\begin{matrix} 1 & 2 \\ 0 & 1 \end{matrix}] [\begin{matrix} 1 & 3 \\ 0 & 1 \end{matrix}] . . . . . . . . [\begin{matrix} 1 & n \\ 0 & 1 \end{matrix}] = [\begin{matrix} 1 & \frac{n (n + 1)}{2} \\ 0 & 1 \end{matrix}] = [\begin{matrix} 1 & 378 \\ 0 & 1 \end{matrix}] \Rightarrow \frac{n (n + 1)}{2} = 378 \Rightarrow n = 27$

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Operations of matrix

Remember concepts with our Masterclasses.

If the product of n matrices 110112011301........1n01 is equal to the matrix 137801, the value of n is equal to

110112011301........1n01=1n(n+1)201=137801 ⇒n(n+1)2=378⇒n=27

Ready to Test Your Skills?

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