short tricks to find nullity of matrices |

Описание: short tricks to find nullity of matrices | #shorts
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The nullity of a matrix is the dimension of the null space of A
also called the kernel of A
If A is an invertible matrix
then null space (A) = {0}
The rank of a matrix is the number of non-zero eigenvalues of the matrix
and the number of zero eigen values
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determines the nullity of the matrix
The nullity of a matrix is the dimension of the null space of A
also called the kernel of A

If A is an invertible matrix, then null space (A) = {0}
The rank of a matrix is the number of non-zero eigenvalues of the matrix
mathematics by er ashish kumar
and the number of zero eigenvalues determines the nullity of the matrix
Matrices
Introduction
Matrix
Types of Matrices
Operations on Matrices
Transpose of a Matrix
Symmetric and Skew Symmetric Matrices
Invertible Matrices
The modern theory of sets is considered to have been originated largely by the
German mathematician Georg Cantor (1845-1918)
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His papers on set theory
appeared sometimes during 1874 to 1897
His study of set theory came when he
was studying trigonometric series of the form a1
sin x + a2
sin 2x + a3
sin 3x + ...
He published in a paper in 1874 that the set of real numbers could not be put into
one-to-one correspondence wih the integers From 1879 onwards, he published
several papers showing various properties of abstract sets
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Definition of set in math | sets class 11
A matrix is an ordered rectangular array of numbers or functions.
A matrix having m rows and n columns is called a matrix of order m × n.
[aij]
m × 1 is a column matrix.
[aij]
1 × n
is a row matrix
An m × n matrix is a square matrix if m = n.
A = [aij]
m × m
is a diagonal matrix if aij = 0, when i ≠ j
A = [aij]
n × n
is a scalar matrix if aij = 0, when i ≠ j, aij = k
(k is some
constant), when i = j.
A = [aij]
n × n
is an identity matrix, if aij = 1, when i = j, aij = 0, when i ≠ j
A zero matrix has all its elements as zero.
A = [aij] = [bij] = B if (i) A and B are of same order, (ii) aij = bij for all
possible values of i and j.
α β
γ α−

MATHEMATICS
kA = k[aij]
m × n
= [k(aij)]
m × n
– A = (–1)A
A – B = A + (–1) B
A + B = B + A
(A + B) + C = A + (B + C), where A, B and C are of same order
A is a symmetric matrix if A′ = A
A is a skew symmetric matrix if A′ = –A.
Any square matrix can be represented as the sum of a symmetric and a
skew symmetric matrix.
If A and B are two square matrices such that AB = BA = I, then B is the
inverse matrix of A and is denoted by A–1 and A is the inverse of B.
Inverse of a square matrix, if it exists, is unique
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