The main application of plasmids is as cloning vectors in gene cloning. In gene cloning‚ a fragment of DNA‚ containing the gene to be cloned is inserted into a circular molecule called the “vector” to produce recombinant DNA molecule. Plasmids are one of the most commonly used “vectors” for this purpose. They transport the gene into a host cell‚ such as a bacterium‚ which is said to be transformed with the recombinant molecule. Here‚ these plasmid vectors multiply‚ producing numerous identical copies
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cross product of the vector U = 2i – 3j – k and V = i + 4j – 2k.(3 marks) Given the matrices. 2 5 3 -2 0 A = -3 1 and B = 1 -1 4 4 2 5 5 5 Compute: ATB(3 marks) tr (AB)(1 mark) (e) Determine if (2‚ -1) is in the set generated by = (3‚ 1)‚ (2‚ 2) (5 marks) Question Two (20 marks) Let T: R2 R2 be defined by T(x‚ y) = (x + y‚ x). Show that T is a linear transformation.(7 marks) Find the
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MA2030 589 UNIVERSITY OF MORA TUW A Faculty of Engineering Department of Mathematics B. Sc. Engineering Level 2 - Semester 2 Examination: MA 2030 LINEAR ALGEBRA Time Allowed: 2 hours 2010 September 2010 ADDITIONAL MATERIAL: None INSTRUCTIONS TO CANDIDATES: This paper contains 6 questions and 5 pages. Answer FIVE questions and NO MORE. This is a closed book examination. Only the calculators approved and labeled by the Faculty of Engineering are permitted. This examination
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An Introduction to Linear Programming Steven J. Miller∗ March 31‚ 2007 Mathematics Department Brown University 151 Thayer Street Providence‚ RI 02912 Abstract We describe Linear Programming‚ an important generalization of Linear Algebra. Linear Programming is used to successfully model numerous real world situations‚ ranging from scheduling airline routes to shipping oil from refineries to cities to finding inexpensive diets capable of meeting the minimum daily requirements. In many of these problems
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to determine the potential distribution ux‚y over the plate‚ subject to the following boundary conditions. 5. Show that the equation ∂2u∂x2-1c2∙∂2u∂t2=0 is satisfied by u=fx+ct+F(x-ct) where f and F are arbitrary functions. 6. If ∂2u∂x2=1c2∙∂2u∂t2 and c=3‚ determine the solution u=f(x‚t) subject to the boundary conditions u0‚t=0 and u2‚t=0 for t≥0 ux‚0=x(2-x) and ∂u∂tt=0=0 for 0≤x≤2. 7. The centre
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2 seconds is -1.6g/s 3) b) = = =22 ∴ from seconds the car moves at an average of 22m/s c) t=4 = =16 ∴ The instantaneous rate at 4s is 16m/s 4a) In order to determine the instantaneous rate of change of a function using the methods discussed in this lesson‚ we would use the formula where h will approach 0‚ and the closer it gets to 0 the more accurate our answer will be. 4b) ∴ =1 Therefore‚ = 1 5a) Therefore
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Computer Linear Algebra-Individual Assignment Topic: Image Sharpening and softening (blurring and deblurring). Nowadays‚ technology has become very important in the society and so does image processing. People may not realize that they use this application everyday in the real life to makes life easier in many areas‚ such as business‚ medical‚ science‚ law enforcement. Image processing is an application where signal information of an image is analyzed and manipulated to transform it to a different
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Chapter 1 Vectors‚ Forces‚ and Equilibrium 1.1 Purpose The purpose of this experiment is to give you a qualitative and quantitative feel for vectors and forces in equilibrium. 1.2 Introduction An object that is not accelerating falls into one of three categories: • The object is static and is subjected to a number of different forces which cancel each other out. • The object is static and is not being subjected to any forces. (This is unlikely since all objects are subject to the force
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TOPIC – LINEAR PROGRAMMING Linear Programming is a mathematical procedure for determining optimal allocation of scarce resources. Requirements of Linear Programming • all problems seek to maximize or minimize some quantity • The presence of restrictions or constraints • There must be alternative courses of action • The objective and constraints in linear programming must be expressed in terms of linear equations or inequalities Objective
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MC-B TOPIC; LINEAR PROGRAMMING DATE; 5 JUNE‚ 14 UNIVERSITY OF CENTRAL PUNJAB INTRODUCTION TO LINEAR PROGRAMMING Linear programming (LP; also called linear optimization) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming
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