NIMCET 2015 Question Paper with solutions

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Question : 44 of 120

Marks: +1, -0

A matrix

M_r

is defined as

M_r

=

[\table r,r-1;r-1,r]

r ∊ N , then the value of det

(M_1)

+ dt

(M_2)

+ ... + det

(m_{2015})

is :

$2014^2$
$2013^2$
2015
$2015^2$

Solution:

We have,

M_r=[\table r,r-1;r-1,r],r∊N

|M_r|=r^2-(r-1)^2

=r^2-r^2+2r-1=2r-1

Now,

|M_1|+|M_2|+|M_3|....|M_{2015}|

⇒1+3+5+7+..+3029

=(2015)^2

[∵

Σ↖{n}↙{n=1}(2n-1)=n^2

]

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