logo

Ask Questions, Get Answers

 
X
 Search
Want to ask us a question? Click here
Browse Questions
Ad
Home  >>  CBSE XII  >>  Math  >>  Determinants
0 votes

Evaluate : $ \begin{vmatrix} 1 & log_ba \\ log_ab & 1 \end{vmatrix}$

$\begin{array}{1 1} 1 \\ -1 \\ \pm 1 \\ 0 \end{array}$

Can you answer this question?
 
 

1 Answer

0 votes
Toolbox:
  • If $A= \begin{bmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{bmatrix}$
  • Then $|A|=a_{11} \times a_{22}- a_{12} \times a_{21}$
  • $log _b a \times log_ab=1$
Step 1:
Let $\Delta= \begin{vmatrix} 1 & log_ba \\ log_ab & 1 \end{vmatrix}$
on expanding we get
$\Delta= 1\times 1 -log _b ^a \times log_a^b$
But $log _b a \times log_ab=1$
Therefore $\Delta=1-1=0$
Solution:option D is correct

 

answered Apr 3, 2013 by meena.p
edited Apr 3, 2013 by meena.p
 

Related questions

Ask Question
student study plans
x
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App
...