If `A=d i ag\ (2\ -5\ \ \ 9)` , `B=d i ag\ (1\ \ \ \ 1\ -4)` and `C=d i ag\ (-6\ \ \ 3\ \ \ 4)` , find `A-2B` (ii) `B+C-2A` (iii) `2A+3B-5C`

If A=d i ag\ (a\ \ b\ \ c) , show that A^n=d i ag\ (a^n\ \ b^n\ \ c^n) for all positive integer n .

If A=d i ag(1-1 2) and B=d i ag(2 , 3 -1), find A+B ,3A+4Bdot

In a /_\ A B C , A D is the bisector of /_A , meeting side B C at D . (i) If B D=2. 5 c m ,\ \ A B=5c m and A C=4. 2 c m , find D C . (ii) If B D=2c m ,\ \ A B=5c m and D C=3c m , find A C . (iii) If A B=3. 5 c m , A C=4. 2 c m and D C=2. 8 c m , find B D .

If a = 3x - 5y, b = 6x + 3y and c = 2y - 4x . Find : (i) a + b - c , (ii) 2a - 3b + 4c .

If points A(5,\ p),\ \ B(1,\ 5),\ \ C(2,\ 1) and D(6,\ 2) form a square A B C D , then p= (a) 7 (b) 3 (c) 6 (d) 8

(i) If 3A = 4B = 6C , find : A : B : C . (ii) If 2a = 3b and 4b = 5c , find: a : c .

If A B=7. 5 c m\ a n d\ C D=2. 5 c m , construct a segment whose length is equal to (i) A B-C D (ii) 2A B (iii) 3C D (iii) A B+C D (v) 2A B+3C D

Multiply: -6a^2b c ,2a^2b\ a n d-1/4 (ii) 4/9a^5b^2,\ 10 a^3b\ a n d\ 6

If A=[{:(,5,4),(,3,-1):}], B=[{:(,2,1),(,0,4):}] and C=[{:(,-3,2),(,1,0):}] , find : (i) A+C (ii) B-A (iii) A+B-C

In a /_\ A B C , A D is the bisector of /_A , meeting side B C at D . (i) If AB=10 cm , AC=14 cm and BC=6cm , find B D and D C (ii) If A C=4. 2 c m , D C=6c m and B C=10 c m , find A B . (iii) If A B=5. 6 c m , A C=6c m and D C=3c m , find B C .