3. If (A=begin{bmatrix}1 & 2 \ 4 & 2end{bmatrix}), then show that |2A|=4|A|.
Determinants
Exercise 4.1
Class 12
Determinants
Exercise 4.1
Evaluate the determinants in Exercise 1 and 2.
1. (begin{vmatrix}2 & 4 \ -5 & -1end{vmatrix})
2. (i) (begin{vmatrix}cosθ & -sinθ \ sinθ & cosθend{vmatrix})
(ii) (begin{vmatrix}x^2-x+1 & x-1 \ x+1 & x+1end{vmatrix})
3. If (A=begin{bmatrix}1 & 2 \ 4 & 2end{bmatrix}), then show that |2A|=4|A|.
4. If (A=begin{vmatrix}1 & 0 & 1 \ 0 & 1 & 2 \ 0 & 0 & 4 end{vmatrix}), then show that |3A|=27|A|.
(i) (begin{vmatrix}3 & -1 & -2 \ 0 & 0 & -1 \ 3 & -5 & 0 end{vmatrix})
(ii) (begin{vmatrix}3 & -4 & 5 \ 1 & 1 & -2 \ 2 & 3 & 1 end{vmatrix})
(iii) (begin{vmatrix}0 & 1 & 2 \ -1 & 0 & -3 \ -2 & 3 & 0 end{vmatrix})
(iv) (begin{vmatrix}2 & -1 & -2 \ 0 & 2 & -1 \ 3 & -5 & 0 end{vmatrix})
6. If (A=begin{vmatrix}1 & 1 & -2 \ 2 & 1 & -3 \ 5 & 4 & -9 end{vmatrix}), find |A|.
(i) (begin{vmatrix}2 & 4 \5 & 1 end{vmatrix})=(begin{vmatrix}2x & 4 \6 & x end{vmatrix})
(ii) (begin{vmatrix}2 & 3 \4 & 5 end{vmatrix})=(begin{vmatrix}x & 3 \2x & 5 end{vmatrix})
