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

If A="diag "[2,-5,9],B="diag "[-3,7,14]" and "C="diag "[4,-6,3] , find: (i) A+2B1 (ii) B+C-A (iii) 2A+B-5C.

If A : B = 1 : 2 , B: C = 3: 4 and C: D = 5 : 6 find D: C : B :A

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=[1 4 7 2 6 5 3-1 2] a n d B=d i ag(125) , then trace of matrix A B^2 is (a)74 (b)75 (c)529 (d)23

Find : (a) 1/2 of (i) 24 (ii) 46 (b) 2/3 of (i) 18 (c) 27 (d) 3/4 of (i) 36 (d) 4/5 of (i) 20 (ii) 35

(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

If A : B = 1 : 2, B : C = 3 : 4 and C : D = 5 : 6, then find the value of D : C : B.