Determinants of Matrices
This lesson covers how to find the determinant of a 2x2 matrix using cross multiplication. It also explains the determinant of a 3x3 matrix using Kramer's rule and the co-factor technique.
- 14:29 “So, to find the co-factors, we have C1 is equal to C1 half plus minus, so we have to take that as a minus plus. So, C1 here will be equal to 3, and the C2, C2 will be equal to minus 4, C3 will be equal to a C3, that is m...”
- 02:21 “We can consider three by three matrices, and dealing with three by three matrices, the determinants for three by three matrices, we need to look at two major aspects, which is the Kramas rule and the Saras rule. Let's lo...”
- 15:14 “find the value of the transpose. So, let's see how we can get, we have gotten the co-factors of A. So, let's write it out, we have A co-factors, A C is equal to C1 is 3, and the C2 is minus 4, C3 is minus 2, C4 is 1. So,...”
Whole Numbers and Prime Factorization
This lesson covers the expression of whole numbers and decimal numbers in standard form. It includes finding prime factors of numbers up to 200, determining the least common multiple (LCM), and finding the highest common factor (HCF). Additionally, it addresses perfect squares and square roots using
- 14:49 “the itself is the IS common factor, IS common factor, what are the IS common factors, we have two, the common between them, stock it up, two, common between them, two also is common, two times two, times what do I begin,...”
- 18:19 “but if you look at it, within the three, these three only appears, did not appear anymore, two, it cannot be the IS common, so looking through the process, the IS, the HCF of this, will give us two times two, which is wh...”
- 16:30 “could have given you a very good idea, now let's pick up one more, one more, let's look into one more, to be able to let's say find the is common factor of 24, 36, and 54, find the is common factors of 24, 36, and 54, no...”
Factorization of Algebraic Expressions
This lesson covers the factorization of simple algebraic expressions and quadratic expressions. It includes methods for identifying factors and solving related word problems.
- 11:43 “Taking it out, what's common in the 3 process? In the 3 process, if you are very observant, you will see 2, 2 connecting to this and 2 connecting to this. They make it more easier. You will see an x, yeah, connecting to...”
- 02:19 “and signs are in the two. So, when the sign comes in, it's factorization. That is, if you are grouping them to the way they belong or you are trying to collect them together. So, factorization, we have factorize 5xy plus...”
- 03:04 “First, pick the first one. Let's pick the first one. We have 5xy, what are the elements or what are the factors that mix up 5xy? Now, the factors that make up 5xy include 1, 5, 2 factor that mix up is 2. 1 is 5 multiplie...”
Polynomials and Their Properties
This lesson covers the definition of polynomials and their degrees. It explains how to divide a polynomial by another polynomial of lesser degree and introduces the remainder theorem. Additionally, it discusses how to find factors of polynomials and solve cubic equations using their roots.
- 20:24 “Mean that a factor of p of x, a factor of p1 of x, mean that if this factor can also be used to divide what. It's just like when you have 4, what are the factors of 4? 1, 2 and 4 itself. And 1, 4, 2 can be used to divide...”
- 21:16 “we are given our p of x. Let's say p of x equals x plus 2 for example. And we want to make this one. We want to say that p minus 2, you know, is to give us what? Minus 2 plus 2 equals 0. So this x plus 2 would be a facto...”
- 11:32 “plus 6. And it's a 0 polynomial is when our p of x equals 0. So, it means when p of x equals 0, and our p of x is this. So, it means this implies that x squared minus 5x plus 6 equals 0. So, this is the 0 polynomials. So...”
Solving Linear and Quadratic Equations
This lesson covers the methods for solving simultaneous linear and quadratic equations using substitution. It explains the definitions of linear and quadratic equations and demonstrates how to manipulate these equations to find solutions.
- 20:13 “And here we have negative. So you multiply through by minus one. And this give you y square plus 10 y minus 24 is equals to zero. Multiply true by minus one. Now you cannot factorize. The coefficient of y is one, you hav...”
- 05:03 “it returns to negative, if it is positive. But if it is negative, it returns to positive. Now, factorize. The coefficient of S square is one, and your constant is minus 12. So you are looking for a number that you multip...”
- 14:42 “Some of minus two and minus five will give you minus seven. Substitute this into the equation. There you have X square minus two X minus five X plus 10 is equals to zero. Don't forget your grouping, bring it together. Wh...”
Roots of Quadratic Equations
This lesson covers how to find the sum and product of the roots of a quadratic equation. It also explains how to form a quadratic equation given the roots and states the conditions for equal roots, real roots, and no roots. Additionally, it discusses the relationship between a line and a curve in te
- 16:51 “Our roots are actually minus five, minus two over five, and minus one over one, oh, number one over two. So if I have this to be minus then, I should have, excuse me, I should have gotten this to be plus, all right? So t...”
- 23:24 “so that you don't deal with like numbers. So that gives me x squared, two over six could lead me to minus one over three. So I have x over three, all right? And 20 over six could lead me to 10 over three, and that would...”
- 03:15 “I have X squared for my X times X. And for my X times minus beta, I'm gonna have X minus X beta. If I go to expand using the minus alpha to multiply, that is minus alpha times X, that gives me alpha minus alpha X. And if...”
Exponential Equations
This lesson covers the definition and properties of exponential equations. It explains how to solve exponential equations of linear form by ensuring the bases are the same. Examples are provided to illustrate the process of finding the unknown variable in these equations.
- 06:18 “two raised to power x or raised to power two. We use what we call the power law yeah. So minus six raised to power two raised to power x plus eight equals zero. So let's why equals two raised to power x. So it means wher...”