Matrix Operation (Shortcut technique)

 

There are different types of matrices - zero matrix, square matrix, scalar matrix, corn matrix, rectangle matrix, singular matrix, triangular matrix, circular matrix, orthogonal matrix, nonzero matrix, invariant matrix, transpose matrix, symmetric matrixConjugate matrix, inverse matrix, orthogonal matrix etc.A matrix is ​​basically a rectangular shape. The famous mathematician James Joseph Sylvester proposed this matrix in 1850. But after 7 years it was fully revealed. That is why he is called the father of the matrix. However, it is also widely used in physics. It is widely used in the mechanics branch of physics. And there the physicist Heisenberg started using the first matrix. . In 1925 he applied it to mechanics. We get an idea about the matrix in the 11th-12th class of the education curriculum of Bangladesh. There we only know the basic concepts and definitions of matrices. Matrices are usually of different dimensions. But before that, we need to know how the elements of the matrix are arranged. Matrices are usually arranged in rectangles and squares. A matrix consists of rows and columns. If I write a structure

row1 [ C1 C2 C3 ] Here 'C' means three columns. Then row1 means the first row. Again r1 |

| r2 | | r3 |

 There are three rows in one column. Then [row × column] is the dimension of a matrix. So let's give an example of a matrix.

Application of matrices: Addition, subtraction, multiplication of matrices can be done.

Addition:- To add matrix we will do (r+c).

For example:

Subtraction: - r-c will subtract in this form

For example:

Multiplication: r×c i.e. r1×c1, r2×‌c2, r3×c3

For example:

Determining the matrix inverse of a matrix is ​​very important:

If A is a matrix |A| That is, if the value of the matrix is ​​non-zero, its inverse matrix can be obtained. But the formula will be A= Adj( A) / |A| , where |A|=0 is not.

Again, it is important to determine the rank of a matrix. rank can be row and column. Mathematician Echalon devised this method. He gives the rules for determining the rank in three conditions.

Condition three: Any non-zero matrix will have leading values. The value below and to the left of each leading value must be zeroIf the first value of the first row is the leading value, then the value of that column of the 2nd row will be zero and will gradually go to the right, but there is no problem if there are multiple zeros. If so, the rows with non-zero entries will be the row rank of the matrix. Again, if you transpose this echelon size, the non-zero column of the matrix that will be found is the Rank column of that matrix. Search Matrix on this website to know all about Matrix. Also visit and follow our website to get all the techniques of Physics Higher Maths together. Here is a thorough explanation of all the subjects of the Physics Department of Hons. You can browse and search our website to read all the articles and hopefully you will get all the tutorials and shortcut techniques for free. thank you

There are different types of matrices - zero matrix, square matrix, scalar matrix, corn matrix, rectangle matrix, singular matrix, triangular matrix, circular matrix, orthogonal matrix, nonzero matrix, invariant matrix, transpose matrix, symmetric matrixConjugate matrix, inverse matrix, orthogonal matrix etc.A matrix is ​​basically a rectangular shape. The famous mathematician James Joseph Sylvester proposed this matrix in 1850. But after 7 years it was fully revealed. That is why he is called the father of the matrix. However, it is also widely used in physics. It is widely used in the mechanics branch of physics. And there the physicist Heisenberg started using the first matrix. . In 1925 he applied it to mechanics. We get an idea about the matrix in the 11th-12th class of the education curriculum of Bangladesh. There we only know the basic concepts and definitions of matrices. Matrices are usually of different dimensions. But before that, we need to know how the elements of the matrix are arranged. Matrices are usually arranged in rectangles and squares. A matrix consists of rows and columns. If I write a structure

row1 [ C1 C2 C3 ] Here 'C' means three columns. Then row1 means the first row. Again r1 |

| r2 | | r3 |

 There are three rows in one column. Then [row × column] is the dimension of a matrix. So let's give an example of a matrix.

Application of matrices: Addition, subtraction, multiplication of matrices can be done.

Addition:- To add matrix we will do (r+c).

For example:

Subtraction: - r-c will subtract in this form

For example:

Multiplication: r×c i.e. r1×c1, r2×‌c2, r3×c3

For example:

Determining the matrix inverse of a matrix is ​​very important:

If A is a matrix |A| That is, if the value of the matrix is ​​non-zero, its inverse matrix can be obtained. But the formula will be A= Adj( A) / |A| , where |A|=0 is not.

Again, it is important to determine the rank of a matrix. rank can be row and column. Mathematician Echalon devised this method. He gives the rules for determining the rank in three conditions.

Condition three: Any non-zero matrix will have leading values. The value below and to the left of each leading value must be zeroIf the first value of the first row is the leading value, then the value of that column of the 2nd row will be zero and will gradually go to the right, but there is no problem if there are multiple zeros. If so, the rows with non-zero entries will be the row rank of the matrix. Again, if you transpose this echelon size, the non-zero column of the matrix that will be found is the Rank column of that matrix. Search Matrix on this website to know all about Matrix. Also visit and follow our website to get all the techniques of Physics Higher Maths together. Here is a thorough explanation of all the subjects of the Physics Department of Hons. You can browse and search our website to read all the articles and hopefully you will get all the tutorials and shortcut techniques for free. thank you