`E = (A^2 B^3) / C^4` if `%A = 2`, `%B = 1`, `%C = 3`. Find `%E`

Let U= {1, 2, 3, 4, 5, 6, 7, 8,9}, A={1, 2, 3, 4}, B = {2, 4, 6, 8) and C={3, 4, 5, 6}. Find (B-C)'

If A : B = 1 : 2, B : C = 3 : 4, C : D = 2 : 3 and D : E = 3 : 4, then what is B : E equal to ?

In Fig. 4.95, if /_A D E=/_B show that A D E ~ A B C . If A D=3. 8 c m , A E=3. 6 c m , B E=2. 1 c m and B C=4. 2 c m , find D E . (FIGURE)

In a A B C , D and E are points on the sides A B and A C respectively such that D E B C If A D=8x-7, D B=5x-3, A E=4x-3 and E C=(3x-1) , find the value of x . (ii) If A D=4x-3, A E=8x-7, B D=3x-1 and C E=5x-3 , find the volume x . (iii) If A D=2. 5 c m , B D=3. 0 c m and A E=3. 75 c m , find the length of A C .

If A=[(2, 2), (-3, 1), (4, 0)], B=[(6, 2), (1, 3), (0, 4)], find the matrix C such that A + B + C is zero matrix.

If A=[(2, 3),( 5 ,7)] , B=[(-1 ,0, 2),( 3, 4, 1)] , C=[(-1, 2 ,3),( 2 ,1, 0)] , find A+B and B+C (ii) 2B+3A and 3C-4B .

In a A B C , D and E are points on A B and A C respectively such that D E// B C . If A D=2. 4 c m ,\ \ A E=3. 2 c m ,\ \ D E=2c m and B C=5c m , find B D and C E .

if A =diag[2 -3 4], B= diag[3 1 -2 )and C= diag[-1 2 2] then find 2A-B+3C.

If A = [{:(2, -3), (4, 1):}], B = [{:(2, 3), (5, 0):}]" and " C = [{:(-1, 2),(0, 5):}] then find A(B + C).