From Basic to Advanced: Learn Matrix Algebra

Name: From Basic to Advanced: Learn Matrix Algebra
Rating: 4.1 (23 reviews)

Learn Matrices in simplest way. We'll learn the concept & together solve many tricky problems :)

Created byAMS Maths

Last updated 9/2017

English

What you'll learn

You can solve all questions on matrix and determinant asked in various competitive exams as well as in academics.

Course content

4 sections • 19 lectures • 3h 11m total length

Definition of a Matrix5:57
Define a matrix as a rectangular arrangement of numbers in rows and columns, and explore basic algebraic operations: addition, subtraction, multiplication, and division by a scalar, and determinants.
Type of Matrices - 16:54
Define matrices as rectangular arrays of rows and columns with order m by n; show square matrices have equal rows and columns, illustrated by 3 by 3 and principal diagonal.
Type of Matrices - 27:10
Discover diagonal matrices with nonzero diagonal elements and zero off-diagonal elements, learn scalar matrices as equal diagonal entries, and identify the identity matrix for a given order.
Type of Matrices - 38:07
Identify upper triangular matrices by recognizing a square matrix with nonzero diagonal elements and zeros below the diagonal, as shown in the 3×3 example.
Type of Matrices - 45:20
Explore type of matrices, including square, diagonal, identity, and rectangular matrices, and practice basic algebraic operations like addition, multiplication, and subtraction.

Equality of two Matrices and General Representation of a Matrix9:48
Determine when two matrices are equal by ensuring the same size and identical corresponding elements, and learn to represent a matrix by its rows and columns using i and j.
Practice Problems on Equality of Matrices9:12
Practice problems on equality of matrices reinforce the definition: matrices must have the same size and equal corresponding elements. Solve for variables using the presented matrix equations.
Addition of two Matrices10:19
Learn how to add two matrices of the same size by summing corresponding elements, with an example, and review matrix addition's commutative and associative properties.
Subtraction of two Matrices9:37
Learn to subtract two matrices by adding the negation of the second matrix, using element-wise operations and the null matrix, and observe addition’s commutativity.
Multiplication of a Matrix by a scalar9:04
Learn how to multiply a matrix by a scalar, applying the real number rule to every element, with step-by-step examples.
Multiplication of two Matrices13:30
this lecture explains when matrix multiplication is feasible by matching inner dimensions, shows A is m-by-n and B is n-by-p, and that the product is m-by-p.
Properties of Matrix Multiplication13:30
Explore the properties of matrix multiplication, including noncommutativity, associativity, and distributivity, with examples showing AB may not equal BA and AB can be zero without A or B being zero.

Trace of a Matrix13:30
Identify the trace by summing the elements on the principal diagonal of a square matrix. Apply the property trace(A+B)=trace(A)+trace(B) and verify with example matrices.
Transpose of a Matrix13:04
Compute the transpose of a matrix by swapping its rows and columns, turning an m-by-n matrix into an n-by-m matrix.
Properties of Transpose Matrix3:56
Learn the key transpose properties: (A+B)^T = A^T + B^T, and (AB)^T = B^T A^T, with (A^T)^T = A, and prepare for conjugate and transpose-conjugate in the next lecture.

Basic Problems on Matrices Set 112:56
Solve basic matrix problems by equating two matrices to determine x, y, and z, and practice addition, subtraction, and B minus C calculations.
Practice Problems on Matrices - Set 2A11:13
Solve matrix equations and practice matrix multiplication to determine the unknown X, verify dimensions, and assess the feasibility of products in Set 2A.
Practice Problems on Matrices - Set 2B13:13
Practice solving matrix multiplication problems from set 2B, computing products of matrices, checking feasibility, and finding powers like square and cube to reinforce the application of matrix multiplication.
Practice Problems on Matrices - Set 315:19
Continue solving matrix problems, focusing on unit (identity) matrices, squaring matrices, and comparing results with scalar multiples. Practice covers multiplying, transposing, and verifying relationships such as B+Q and B−Q.

Requirements

You should know basic Algebraic operations and then you are all set to start this course.

Description

This course is designed to cover all the basic and advanced concepts starting with 9th Grade to Undergraduate Level. First, we will discuss Matrices and next Determinants. We will also solve good number of questions on each and every topic. I will keep on adding additional topics and always keep the course up to date. I will answer your queries within 24 hours so feel free to post your queries and keep your concepts crystal clear.

Who this course is for:

You might be a 9th Grade or 10th Grade student or may be pursuing an engineering course. You all have to learn Matrix and Determinant to solve tough questions in easy way. This course will help you :)

From Basic to Advanced: Learn Matrix Algebra

What you'll learn

Explore related topics

Course content

Introduction5 lectures • 33min

Algebraic Operation on Matrices7 lectures • 1hr 15min

Important terms related to Matrices3 lectures • 31min

Practice Problems on Matrices4 lectures • 53min

Requirements

Description

Who this course is for: