“Business Mathematics” MATH-161-1 Lecture 11 “Mathematic of Finance-I (A)”

[Audio] Welcome everyone to this session on Business Mathematics. Today's lecture will cover the concept of Vectors. Vectors are used to represent lines in a plane, and can be described by an ordered pair of coordinates. We will discuss the various properties and applications of Vectors, and how they can be used to solve mathematical problems. So, let's get started!.

[Audio] A vector is a mathematical object with both magnitude and direction. Examples include position, velocity, momentum, and force. We'll be discussing how to add, subtract, multiply, and divide vectors, and how these operations can be used to solve mathematical problems. Let's get started..

[Audio] An order pair of numbers written in parenthesis represents a point in a plane, which can be used to measure the distance between two points. A vector is an object that has both a magnitude and a direction and can be used to represent the magnitude and direction of a movement. In business mathematics, vectors can be used to help understand and measure different movements..

[Audio] Lesson is on vectors. A vector is a line segment with length and direction. Pythagorean theorem can be used to calculate length. Two-dimensional vector is typically represented with two coordinates, like [x,y]. Important in business math, this tool is useful for direction and distance situations. Looking forward to discussing vectors..

[Audio] Vectors are elements that can be used to represent physical quantities such as position, direction and velocity. The elements 'x' and 'y' are the components of the vector. For example, 'a' and 'b' are two component row vectors, 'a' being [2, 5] and 'b' being [7, 3] and 'c' and 'd' are three component column vectors. Understanding the basics of vectors is fundamental in the field of business mathematics..

[Audio] We will be exploring vectors, a concept used in mathematics to represent objects that have magnitude and direction. Our focus will be on vector addition and how to apply it in order to solve problems. For example, when we add two component vectors a and b, given by a = [2, 5] and b = [7, 3] respectively, we can visualize the addition by adding the corresponding components of each vector to get a single vector of the sum. That is, a + b = [2, 5] + [7, 3] = [2 + 7, 5 + 3] = [9, 8]. With this, we can easily observe the operations of vector addition and use it to tackle more complex problems..

[Audio] We can add two or more vectors by adding their components together. For instance, c's components are three, seven, and nine while d's components are two, five, and four. When we add c and d, the components of the resulting vector are five, twelve, and thirteen. That is the addition of vectors in a nutshell..

[Audio] Let's take a look at vectors and their subtraction operations. Subtraction with vectors works the same way as with addition, with the only difference being that you subtract rather than add. As an example, vector d is 2, 5 and 4 and vector c is 3, 7 and 9. To subtract them, we simply subtract the corresponding components from each other yielding 1, 2 and 5 as the answer. Understanding vector subtraction can be tricky, but this example should make the operation a bit more clear..

[Audio] Vector multiplication by a real number involves multiplying each component of the vector by the scalar. As an example, if the vector is 3, 7, and 4, and the scalar is 2, the product would be 6, 14, and 8. Therefore, it is a straightforward operation that yields a vector with the same number of components and the same arrangement..

[Audio] Explaining the multiplication of a vector by another vector requires both vectors to have the same number of components. As an example, consider a row vector a = [2, 5, 4] and a column vector b = [4, 2, 3]. The product of these two vectors is calculated by multiplying each component of vector a by the corresponding component of vector b and then summing the results. Therefore, a . b = [2, 5, 4] . [4, 2, 3] = 2 x 4 + 5 x 2 + 4 x 3 = 8 + 10 + 12 = 30..

[Audio] Explored concept of vectors and how they can provide a simple way of recording data and performing fundamental arithmetical operations on it. Looked at how a simple equation can be expressed in vector form, and how to multiply two vectors together. Discussed how vectors can be used to represent and solve higher-dimensional problems. Gained a better understanding of the use of vectors in business mathematics. Thank you for your attention..