**The beginnings of matrices and determinants goes back to the second century BC** although traces can be seen back to the fourth century BC. However it was not until near the end of the 17th Century that the ideas reappeared and development really got underway. There are two fields whose total area is 1800 square yards.

Matrices represent **functions between spaces, called vector spaces, and not just any functions either, but linear functions**. This is in fact why linear algebra focuses on matrices.

In the passage above he notes that **from an m by n array of numbers — what he calls a Matrix — we can take p columns and rows to create squares from which we can produce determinants**. That is, the m by n array gives birth to the objects he is interested in. And so that's where it comes from!

Matrices are used very often in **3D geometry** (e.g. computer graphics) and are very powerful. A simple 4x4 matrix can represent a lot of transformations at once (translation, rotation, scaling, perspective/orthogonal projection).

**To multiply a matrix by a single number is easy:**

- These are the calculations: 2×4=8. 2×0=0.
- The "Dot Product" is where we multiply matching members, then sum up: (1, 2, 3) • (7, 9, 11) = 1×7 + 2×9 + 3×11. = 58.
- (1, 2, 3) • (8, 10, 12) = 1×8 + 2×10 + 3×12. = 64.
- DONE! Why Do It This Way?

Matrices can be solved physical related application and one applied in the study of electrical circuits, quantum mechanics and optics, with the help of matrices, calculation of battery power outputs, resistor conversion of electrical energy into another useful energy, these matrices play a role in calculation, with the

Matrices. Matrices allow explicit manipulation of finite-dimensional vector spaces and linear maps. **Their theory is thus an essential part of linear algebra**.

Matrices are **used in the science of optics to account for reflection and for refraction**. Matrices are also useful in electrical circuits and quantum mechanics and resistor conversion of electrical energy. Matrices are used to solve AC network equations in electric circuits.

In chemical analysis, matrix refers to **the components of a sample other than the analyte of interest**. The matrix can have a considerable effect on the way the analysis is conducted and the quality of the results are obtained; such effects are called matrix effects.

**The beginnings of matrices and determinants goes back to the second century BC** although traces can be seen back to the fourth century BC. However it was not until near the end of the 17th Century that the ideas reappeared and development really got underway. There are two fields whose total area is 1800 square yards.

When we work with matrices, we refer to real numbers as scalars. The term scalar multiplication refers to the product of a real number and a matrix. In scalar multiplication, **each entry in the matrix is multiplied by the given scalar**. In contrast, matrix multiplication refers to the product of two matrices.

**Algebra of Matrices is the branch of mathematics**, which deals with the vector spaces between different dimensions. The innovation of matrix algebra came into existence because of n-dimensional planes present in our coordinate space.

A matrix consists of rows and columns. These rows and columns define the size or dimension of a matrix. The various types of matrices are **row matrix, column matrix, null matrix, square matrix, diagonal matrix, upper triangular matrix, lower triangular matrix, symmetric matrix, and antisymmetric matrix**.

**Matrix theory is the specialization of linear algebra** to the case of finite dimensional vector spaces and doing explicit manipulations after fixing a basis.

**The important chapters covered in the question paper are;**

- Integration.
- Complex Numbers.
- Matrices and Determinants.
- Circle.
- 3D Geometry.
- Binomial Theorem.
- Application of Derivatives.
- Probability and Statistics.

JEE Main 2022 Mathematics Syllabus

S.No. | Units |
---|---|

1 | Sets, Relations and Functions |

2 | Complex Numbers and Quadratic Equations |

3 | Matrices and Determinants |

4 | Permutations And Combinations |

**JEE Main Algebra Syllabus**

- UNIT 1: Complex Numbers and Quadratic Equations.
- UNIT 2: Matrices and Determinants.
- UNIT 3: Permutations and Combinations.
- UNIT 4: Mathematical Induction and Reasoning.
- UNIT 5: Binomial Theorem.
- UNIT 6: Sequences and Series.
- UNIT 7: Statistics and Probability.
- Measures of Dispersion.

JEE Main Mathematics Syllabus 2022

Unit No | Topic's Name |
---|---|

1. | Sets, Relations, and Functions |

2. | Complex Numbers 7 Quadratic Numbers |

3. | Matrices and Determinants |

4. | Permutations & Combinations |

The Greek mathematician **Menaechmus** (middle fourth century B.C.) is credited with discovering that the parabola is a conic section. He is also credited with using parabolas to solve the problem of finding a geometrical construction for the cubed root of two.

**Aristotle** is considered by many to be the first scientist, although the term postdates him by more than two millennia. In Greece in the fourth century BC, he pioneered the techniques of logic, observation, inquiry and demonstration.

**The important chapters covered in the question paper are;**

- Integration.
- Complex Numbers.
- Matrices and Determinants.
- Circle.
- 3D Geometry.
- Binomial Theorem.
- Application of Derivatives.
- Probability and Statistics.

Dated : 25-May-2022

Category : Education