PPT-In this chapter we will learn about vectors.

properties addition components of vectors When you see a vector think components Multiplication of vectors will come in later chapters Vectors have magnitude and direction Chapter 3 Vectors. It is essential that you do some reading but the topics discussed in this chapter are adequately covered in so many texts on linear algebra that it would be arti64257cial and unnecessarily limiting to specify precise passages from precise texts The 1 Motivation A3 A2 Vectors A3 A21 Notational Conventions A4 A22 Visualization A5 A23 Special Vectors A5 A3 Vector Operations A5 A31 Transposition A6 A32 Equality A6 A33 Addition and Subtraction define . scalar and vector quantities and . give . examples.. (. b) draw and use a vector triangle to . determine the resultant of two vectors such as displacement, velocity and force.. (c) Use trigonometry to determine the resultant of two vectors.. Section 3.4. Bases for Subspaces. Spanning Sets. Let . W. be a subspace of . , and . a set of vectors in . W. (. i.e. . ). The set . S. is a . spanning set . for . W. (or . S. . spans. . W. ) if and only if every vector in . A . scalar. quantity . can be described by a . single number. , . with some meaningful . unit. 4 oranges. 20 miles. 5 miles/hour. 10 Joules of energy. 9 Volts . Vectors and scalars. A . scalar. quantity . Motivating Question. : An Airplane flies north with an airspeed of 575 mph. If the wind is blowing 30° north of east at 50 mph, what is the speed of the plane as measured from the ground? What if the wind blew south of west?. By Janice Marriott & Peter . Lubach. (Big Cats). Look at the front cover and read the back blurb. . 1. What are 2 things you think you will learn about in this book? . Re-read p. 14-15 about why balls bounce. . Vector Spaces. MATH . 264 Linear . Algebra. Introduction. There are two types of physical quantities:. Scalars = quantities that can be described by numerical value alone (Ex: temperature, length, speed). Vectors, Shmectors. Objectives. 1. Distinguish between a scalar and a vector.. 2. Add and subtract vectors by using the graphical method.. 3. Multiply and divide vectors by scalars.. Vectors, Schmectors. Any vector can be resized by multiplying it by a real number (scalar).. Multiplying by positive scalar changes magnitude only.. Multiplying by a negative scalar changes the magnitude and its direction.. 4.1 Vectors in . R. n. 4.2 Vector Spaces. 4.3 Subspaces of Vector Spaces. 4.4 Spanning Sets and Linear Independence. 4.5 Basis and Dimension. 4.6 Rank of a Matrix and Systems of Linear Equations. A vector is a DNA molecule that has the abil­ity to replicate autonomously in an appropri­ate host cell and into which the gene of inter­est (a foreign genetic sequence) is integrated. When we insert a foreign genetic sequence into the vector the aim is either to obtain numer­ous copies of the gene of interest or to obtain the product of that.. or phages are viruses that specifically infect bacteria. . Viral vectors are those in which gene of interest is incorporated in the genome of virus.. The phage particle attaches to the outer surface of bacterium and injects its DNA into the cell.. Examples:. Viral transduction into mammalian cells. Agrobacterium transformation of plant cells. Sources: . http://en.wikipedia.org/wiki/Viral_vector. Daniel . Eisenman. , Medical University of South Carolina.