Identity or Unit Matrix
A square matrix A=[a i j ] n x n is called an identity or unit matrix if (2) a i j =1 for all i = j In other words a square matrix each of whose diagonal elements is unity and each of whose non-diagonal elements is equal to zero is called an identity..
A square matrix A=[a i j ] n x n is called an identity or unit matrix if (2) a i j =1 for all i = j In other words a square matrix each of whose diagonal elements is unity and each of whose non-diagonal elements is equal to zero is called an identity..Matrices and Determinants Summary
[A i j ] where A i j is the co-factor of the element a i j . Adjoint of A is denoted by Adj A. Note that the concept of adj is only for square matrix. A square matrix A is said to be non-singular if |A| 0. Let A be a square matrix of order n. If there exists a square m..
[A i j ] where A i j is the co-factor of the element a i j . Adjoint of A is denoted by Adj A. Note that the concept of adj is only for square matrix. A square matrix A is said to be non-singular if |A| 0. Let A be a square matrix of order n. If there exists a square m..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 j..
Diagonal Matrix
A square matrix A=[a i j ] n x n is called a diagonal matrix if all the elements, except those in the leading diagonal, are zero. i.e., a i j = 0 for all i j..
A square matrix A=[a i j ] n x n is called a diagonal matrix if all the elements, except those in the leading diagonal, are zero. i.e., a i j = 0 for all i j..Skew-Symmetric Matrix:
A square matrix A = [a i j ] is said to be skew-symmetric if the (i,j) t h element of A is the negative of the (j,i) t h element of A i.e., if a i j = -a j i for all i, j. In particular, for i = j, we have Thus the ..
A square matrix A = [a i j ] is said to be skew-symmetric if the (i,j) t h element of A is the negative of the (j,i) t h element of A i.e., if a i j = -a j i for all i, j. In particular, for i = j, we have Thus the ..Adjoint and Inverse of a Matrix
Adjoint of a Square Matrix - The adjoint of a square matrix [a i j ] is defined as the transpose of the matrix [A i j ] where A i j are the cofactors of the elements a i j . Adjoint of A is denoted by adj ..
Adjoint of a Square Matrix - The adjoint of a square matrix [a i j ] is defined as the transpose of the matrix [A i j ] where A i j are the cofactors of the elements a i j . Adjoint of A is denoted by adj ..Question 7
Question: Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Find the number of words which have atleast one letter repeated. Answer: Total number of 5 letter words from given 10 letters = 10 5 (if ..
Transpose of a Matrix
The transpose of a matrix A is got by interchanging its rows and columns and is denoted by A' or A T . If A = [a i j ] m x n is a matrix of order mxn, the transpose of A = A' = [a j i ] n x m is a matrix of order n..
The transpose of a matrix A is got by interchanging its rows and columns and is denoted by A' or A T . If A = [a i j ] m x n is a matrix of order mxn, the transpose of A = A' = [a j i ] n x m is a matrix of order n..Question 9
Question: How many words of different 4 letters can be formed out of 7 capital letters, 3 vowels and 8 consonants, if each word starts with a capital letter and contains at least one vowel? Answer: Any capital letter can be chosen as the first letter of each wor..
Question: How many words of different 4 letters can be formed out of 7 capital letters, 3 vowels and 8 consonants, if each word starts with a capital letter and contains at least one vowel? Answer: Any capital letter can be chosen as the first letter of each wor..Properties of Inverse of Matrix
In other words, a square matrix A is invertible if and only if A is a non-singular matrix. (c) If A and B are invertible square matrices, then (AB) - 1 = B - 1 A - 1 (d) If A and B are two non-singular square matrices of the same order, then AB and BA are also non-singular matr..
In other words, a square matrix A is invertible if and only if A is a non-singular matrix. (c) If A and B are invertible square matrices, then (AB) - 1 = B - 1 A - 1 (d) If A and B are two non-singular square matrices of the same order, then AB and BA are also non-singular matr..See what our Users say :
Tutor was excellent, asnwered the question rapidly and provided the information I needed to understand the problem.
Tutor is the BEST. I have learned a lot from her. I never thought algebra will become my favourate subject. All because of Tutor Vista.
This Tutor Vista is GREAT! loved this session, it helped me heaps.
Thank you very much for helping to me is very important to have my lessons. Because you manage to take good notes in school thank you Tutor Vista
Looking for More Help!
