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 the determinant: $\begin{vmatrix} 3&-1&-2 \\ 0&0&-1 \\3&-5&0 \end{vmatrix}$

Can you answer this question?
 
 

1 Answer

0 votes
Toolbox:
  • To evaluate a matrix of order $3\times 3$
  • $\mid A\mid=\begin{vmatrix}a_{11} & a_{12} & a_{13}\\a_{21} & a_{22} & a_{23}\\a_{31} & a_{32} & a_{33}\end{vmatrix}$
  • Therefore $\mid A\mid=a_{11}(a_{22}\times a_{33}-a_{23}\times a_{32})-a_{12}(a_{21}\times a_{32}-a_{23}\times a_{31})+a_{13}(a_{21}\times a_{32}-a_{22}\times a_{31})$
Given:(i) $Evaluate:\begin{vmatrix}3 & -1 & -2\\0 & 0 &-1\\3 & -5 & 0\end{vmatrix}$
 
We know to evaluate the value of the determinant of order $3\times 3$
 
Therefore $\mid A\mid=a_{11}(a_{22}\times a_{33}-a_{23}\times a_{32})-a_{12}(a_{21}\times a_{32}-a_{23}\times a_{31})+a_{13}(a_{21}\times a_{32}- a_{22}\times a_{31})$
 
$\mid A\mid=3[(0\times 0-(-1\times -5)]-(-1)[0\times 0-(-1\times 31]+(-2)[0\times 0-(0)\times 3]$
 
$\qquad=3(-5)+1(3)-2(0)$
 
$\qquad=-15+3-0$
 
$\qquad=-12$

 

answered Feb 20, 2013 by sreemathi.v
edited Feb 20, 2013 by sreemathi.v
 
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
...