Prove by method of induction ( ll 1 & 2 0 & 1 )^n= ( cc 1 & 2 n 0… - Vidyadip

Question

Prove by method of induction

$\left(\begin{array}{ll}1 & 2 \\ 0 & 1\end{array}\right)^n=\left(\begin{array}{cc}1 & 2 n \\ 0 & 1\end{array}\right) \forall n \in N$

✓

Answer

Get the step-by-step solution for this question inside the Vidyadip app.

Get the answer in the app

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Solve the Following Question.(4 Marks)" from Methods of Induction and Binomial Theorem→Methods of Induction and Binomial Theorem — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

Prove that:
$\cos\frac{\pi}{15}\cos\frac{2\pi}{15}\cos\frac{4\pi}{15}\cos\frac{7\pi}{15}=\frac{1}{16}$

In a village, there are 87 families of which 52 families have at most 2 children. In a rural development programme, 20 families are to be helped chosen for assistance of which at least 18 families must have at most 2 children. In how many ways can the choice be made?

Solve the following equation:
$\sin^{2}\text{x}-\cos\text{x}=\frac{1}{4}$

If $\cos\text{x}=-\frac{3}{5}$ and x lies in the IIIrd quadrant, find the values of $\cos\frac{\text{x}}{2},\sin\frac{\text{x}}{2},\sin2\text{x}.$

Prove that $\sin\text{x}+\sin3\text{x}+...+\sin(\text{2n-1})\text{x}=\frac{\sin ^2\text{nx}}{\sin\text{x}}$ for all $\text{n}\in\text{N}.$

Show that for any sets A and B,$\text{A}\cup(\text{B}-\text{A})=(\text{A}\cup\text{B})$

If $\text{f(x)}=\frac{1}{1-\text{x}},$ show that $\text{f}\big[\text{f}\{\text{f(x)}\}\big]=\text{x}$

Evaluate the following limit:
$\lim\limits_{\text{h}\rightarrow0}\frac{\sqrt{\text{x}+\text{h}}-\sqrt{\text{x}}}{\text{h}},\text{x}\ne0$

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow1}\frac{\sqrt{5\text{x}-4}-\sqrt{\text{x}}}{\text{x}^2-1}$

Find the number of words formed by permuting all the letters of the following words:
RUSSIA.