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Let 0 ! V1 ! ! Vk ! 0 be a long exact sequence of vector spaces with linear maps. Show that P (??1)i dim Vi = 0.
The area of a rectangle gets decreased by 8 m2, if its length is decreased by 5 m and breadth increased by 3 m. If we enhance the length by 3 m and breadth by 2 m, the area is en
We know that 2 4 = 16 and also that 2 is referred to as the base, 4 as the index or power or the exponent. The same if expressed in terms of logarithms would be log 2
If the p th , q th & r th term of an AP is x, y and z respectively, show that x(q-r) + y(r-p) + z(p-q) = 0 Ans: p th term ⇒ x = A + (p-1) D q th term ⇒ y = A + (
what is a liter
Consider the Solow growth model as given in the lecture notes using the Cobb-Douglas production function Y t = AK 1-α t L α t a) Set up the underlying nonlinear differen
Parallel Vectors - Applications of Scalar Multiplication This is an idea that we will see fairly a bit over the next couple of sections. Two vectors are parallel if they have
A bag of 28 tulip bulbs contains 12 red tulip bulbs, 9 yellow tulip bulbs, and 7 purple tulip bulbs. Two bulbs are selected without replacement. Determine, a) The probability th
scanning the demographic environment
Correlation and Regression CORRELATION is an important statistical concept which refers to association or interrelationship among variables. The reasons of studying correla
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