Example:
A = {3, 4, 5, 6}, B = {6, 4, 3, 5} A = B Elements in both sets need not be of same orde..
Minors
Let |aij| be a determinant of order n. The determinant obtained by deleting the i t h row and j t h column in which the element a i j lies is called the minor of element a i j and is denoted by M i ..
Summary
A matrix is a rectangular array of numbers, arranged in rows and columns. Order of a matrix = Number of rows in it x Number of columns in it Row matrix is a matrix with only one row. Column matrix is a matrix with only one column. Zero or Null matrix is a..
Proof:
Let A be any set. In order to prove that f A we must show that there is no element of f which is not present in A. And since f contains no element at all, no such element can be found out. Hence f A...
Matrices
A rectangular array of entries is called a Matrix. The entries may be real, complex or functions. The entries are also called as the elements of the matrix. The rectangular array of entries are enclosed in an ordinary bracket or in square bracke..
Definition of a Matrix
A rectangular array of entries is called a Matrix. The entries may be real, complex or functions. The entries are also called as the elements of the matrix. The rectangular array of entries are enclosed in an ordinary bracket or in square bracket. Matrices are denoted by capital lette..
Definition:
If A and B are any two sets then the relative complement of B in A is the set of all elements in A which are not in B. It is denoted by A - B..
If A and B are any two sets then the relative complement of B in A is the set of all elements in A which are not in B. It is denoted by A - B..Matrices and Determinants
Matrices - A rectangular array of entries is called a Matrix. The entries may be real, complex or functions. The entries are also called as the elements of the matrix. The rectangular array of entries are enclosed in an ordinary bracket or in square bracke..
Subsets
If A and B are sets such that each element of A is an element of B, then we say that A is a subset of B and write A B. ..
If A and B are sets such that each element of A is an element of B, then we say that A is a subset of B and write A B. ..Multiplication of Matrices
Let A be a matrix of order mxn. Let B be a matrix of order nxp. Then the product of the matrices A and B is of order mxp. i.e., when we multiply two matrices the number of columns of the first matrix should be equal to the number of rows of the second matrix. Two matrices can b..
Let A be a matrix of order mxn. Let B be a matrix of order nxp. Then the product of the matrices A and B is of order mxp. i.e., when we multiply two matrices the number of columns of the first matrix should be equal to the number of rows of the second matrix. Two matrices can b.. Result
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