If $$P = \left[ {\matrix{ 1 & 0 \cr {{1 \over 2}} & 1 \cr } } \right]$$, then P50 is :
Solution
$$P = \left[ {\matrix{
1 & 0 \cr
{{1 \over 2}} & 1 \cr
} } \right]$$<br><br>$${P^2} = \left[ {\matrix{
1 & 0 \cr
{{1 \over 2}} & 1 \cr
} } \right]\left[ {\matrix{
1 & 0 \cr
{{1 \over 2}} & 1 \cr
} } \right] = \left[ {\matrix{
1 & 0 \cr
1 & 1 \cr
} } \right]$$<br><br>$${P^3} = \left[ {\matrix{
1 & 0 \cr
1 & 1 \cr
} } \right]\left[ {\matrix{
1 & 0 \cr
{{1 \over 2}} & 1 \cr
} } \right] = \left[ {\matrix{
1 & 0 \cr
{{3 \over 2}} & 1 \cr
} } \right]$$<br><br>$${P^4} = \left[ {\matrix{
1 & 0 \cr
1 & 1 \cr
} } \right]\left[ {\matrix{
1 & 0 \cr
1 & 1 \cr
} } \right] = \left[ {\matrix{
1 & 0 \cr
2 & 1 \cr
} } \right]$$<br><br>$\vdots$<br><br>$\therefore$ $${P^{50}} = \left[ {\matrix{
1 & 0 \cr
{25} & 1 \cr
} } \right]$$
About this question
Subject: Mathematics · Chapter: Matrices and Determinants · Topic: Types of Matrices and Operations
This question is part of PrepWiser's free JEE Main question bank. 274 more solved questions on Matrices and Determinants are available — start with the harder ones if your accuracy is >70%.