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

Let r and n be positive integers such that 1 < r < n. Then prove the following:
$\frac{{^\text{n}}\text{C}_{\text{r}}}{{^\text{n}}\text{C}_{\text{r}-1}}=\frac{\text{n}-\text{r}+1}{\text{r}}$

Find the value of $\frac{3+\log _{10} 343}{2+\frac{1}{2} \log _{10}\left(\frac{49}{4}\right)+\frac{1}{2} \log _{10}\left(\frac{1}{25}\right)}$

Find the eccentricity, coordinates of foci, length of the latus-rectum of the following ellipse:$9\text{x}^2+25\text{y}^2=225$

$\text{a}(\cos\text{B}+\cos\text{C}-1)+\text{b}(\cos\text{C}+\cos\text{A}-1)\\+\text{c}(\cos\text{A}+\cos\text{B}-1)=0$

One diameter of the circle circumscribing the rectangle ABCD is 4y = x + 7. If the coordinates of Aand B are (-3, 4) and (5, 4) respectively, find the equation of the circle.

If $\sin\text{x}+\cos\text{x}=0$ and x lies in the fourth quadrant, find $\sin \text{x } $and $\cos\text{x}.$

If the line segment joining the points $P(x_1, y_1)$ and $Q(x_2, y_2)$ subtends an angle $\alpha$ at the origin $O$, prove that: $\text{O}\text{P}.\text{O}\text{Q}\cos\alpha =\text{x}_1\text{x}_2+\text{y}_1\text{y}_2. $

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

An analysis of the weekly wages paid to workers in two firms A and B, belonging to the same industry gives the following results:

	Firm A	Firm B
No. of wage earners	586	648
Average weekly wages	52.5	47.5
Variance of the	100	121
Distribution of wages

Which firm A or B pays out larger amount as weekly wages?
Which firm A or B has greater variability in individual wages?

Prove that $3 x^2+3 y^2-6 x+4 y-1=0$, represents a circle. Find its centre and radius.