Question

[tex] The value of \left|\begin{array}{ccc}2008 &2009\\2010&2011\end{array}\right| .........,Select Proper option from the given options.

(a) -1

(b) 1

(c) -2

(d) 2
[/tex]

Answer 1

HELLO DEAR,

LET D = $\left|\begin{array}{cc}2008 &2009\\2010&2011\end{array}\right|$

we know if value of determinant is find by
$\left|\begin{array}{cc}a&b\\c&d\end{array}\right|$ = |ad - bc|

therefore, D = $\left|\begin{array}{cc}2008 &2009\\2010&2011\end{array}\right|$

D = |(2008*2011) - (2009*2010)|

D = |(2008)*(2010 + 1) - (2008 + 1)*(2010)|

D = |2008*2010 + 2008 - 2008*2010 - 2010|

D = |2008 - 2010|

D = |-2|

D = 2

HENCE, OPTION (D) is correct,

I HOPE ITS HELP YOU DEAR,
THANKS

Answer 2

$Let A = \left[\begin{array}{ccc}2008&2009\\2010&2011\\\end{array}\right]$

Here, a = 2008, b = 2009, c = 2010, d = 2011.

We know that Determinant of matrix A = |ad - bc|

= > |(2008)(2011) - (2009)(2010)|

= > |4038088 - 4038090|

= > |-2|.

= > 2.

Therefore, the answer is Option (D) = 2.

Hope it helps!