Find the values of a and b, when:
(i) `(a+3,b-2)=(5,1)`
(ii) `(a+b,2b-3)=(4,-5)`
(iii) `((a)/(3)+1,b-(1)/(3))=((5)/(3),(2)/(3))`
(iv) `(a-2,2b+1)=(b-1,a+2)`

Find the product : (i) (x+3)(x^(2)-3x+9) " " (ii) (7+5b)(49-35b+25b^(2)) (iii) (5a+(1)/(2)) (25a^(2)-(5a)/(2)+(1)/(4)) " " (iv) (a+b-2)[a^(2)+b^(2)+4(a+b)+4] .

If a = (sqrt5 + 1)/(sqrt5 + 1) and b = (sqrt5 -1)/(sqrt5 + 1) , then find the value of (a) (a^(2) + ab + b^(2))/(a^(2) - ab + b^(2)) (b) ((a -b)^(3))/((a + b)^(3)) (c) (3a^(2) + 5ab + b^(2))/(3a^(2) - 5ab + b^(2)) (d) (a^(3) + b^(3))/(a^(3) - b^(3))

Find the value of (2.3a^(5)b^(2)) xx(1.2 a^(2)b^(2)) when a = 1 and b = 0.5

Using vectors, find the area of Delta ABC whose vertices are (i) A(1,1,2),B(2,3,5) and C(1,5,5) (ii) A(1,2,3),B(2,-1,4) and C(4,5,-1) (iii) A(3,-1,2),B(1,-1,-3) and C(4,-3,1) (iv) A ( 1,-1,2),B(2,1,-1) and C(3,-1,2).

Compute the indicated products (i) [(a,b),(-b,a)][(a,-b),(b,a)] (ii) [(1),(2),(3)]["2 3 4"] (iii) [(1,-2),(2,3)][(1,2,3),(2,3,1)] (iv) [(3,-1,3),(-1,0,2)][(2,-3),(1,0),(3,1)] .

If a=2 and b=3, then find the values of each of the following: (i) a^a+b^b (ii) a^b+b^a (iii) a^b (a/b)^a (iv) (1/a+1/b)^a

Compute the indicated products: (i) [(a,b),(-b,a)][(a,-b),(b,a)] (ii) [(1),(2),(3)][(2,3,4)] (iii) [(1,-2),(2,3)][(1,2,3),(2,3,1)] (iv) [(2,3,4),(3,4,5),(4,5,6)][(1,-3,5),(0,2,4),(3,0,5)] (v) [(2,1),(3,2),(-1,1)][(1,0,1),(-1,2,1)] (vi) [(3,-1,3),(-1,0,2)][(2,-3),(1,0),(3,1)]

Compute the indicated products: (i) [(a,b),(-b,a)][(a,-b),(b,a)] (ii) [(1),(2),(3)][(2,3,4)] (iii) [(1,-2),(2,3)][(1,2,3),(2,3,1)] (iv) [(2,3,4),(3,4,5),(4,5,6)][(1,-3,5),(0,2,4),(3,0,5)] (v) [(2,1),(3,2),(-1,1)][(1,0,1),(-1,2,1)] (vi) [(3,-1,3),(-1,0,2)][(2,-3),(1,0),(3,1)]

Compute the indicated products: (i) [(a,b),(-b,a)][(a,-b),(b,a)] (ii) [(1),(2),(3)][(2,3,4)] (iii) [(1,-2),(2,3)][(1,2,3),(2,3,1)] (iv) [(2,3,4),(3,4,5),(4,5,6)][(1,-3,5),(0,2,4),(3,0,5)] (v) [(2,1),(3,2),(-1,1)][(1,0,1),(-1,2,1)] (vi) [(3,-1,3),(-1,0,2)][(2,-3),(1,0),(3,1)]