Countable and Non-Countable nouns

Countable nouns are those which can be counted, they also have singular as well as plural forms.
Countable nouns are used with a,an,the,many,few,fewer,number,this,that,every,each, neither,either,those,these,some,any,enough
For example - She made fewer mistakes in the match today

While non-countable or Mass nouns are those which can't be counted and sometime they do not have any plural form.
Non-countable nouns are used with much,less/lesser,this,that,some,any,enough,amount of
For example - Arun have less money than suresh

Some of the nouns can be used as both Countable and non countable ones. It just depends upon how we are using them.
For example-  he got into trouble(non-countable)
                       he had many troubles(countable)

the usage of 's and s'

Apostrophe ( ' ) and letter ( s ) is used to make a noun possessive.

For example - That car is amit's
                        The men's hockey match is tomorrow.

• A singular noun can use 's and s' for same effect. 

For example - The car's speed is slow               correct
                        The cars' speed is slow               correct

• A Plural ending with s takes apostrophe( ' ) to become possessive.

For example - The new buses's are fast              correct
                        The new buses's are fast              incorrect

Common mistakes in Grammer

• The usage of    's and s'

Terms in Linear Algebra

Some important terms related in Linear algebra

• Nul matrix A matrix in which all elements are zero is called Null matrix.
• Row matrix A matrix with 1 row and any no. of column is called Row matrix.
• Column matrix A matrix with 1 column and any no.of row is called column matrix
• Square matrix A matrix having equal no. of rows and columns is called Square matrix.
• Unit matrix A Square matrix in which all diagonol elements are 1 and all non diagonal elements are 0 is called Unit matrix.
• Diagonal Matrix A Square matrix in which all diagonal elements are non zero and non diagonal matrix are 0 is called Diagonal matrix.
• Scalar matrix A diagonal matrix with all diagonal elements are a scalar is called Scalar matrix.
• Symmetric Matrix A matrix which satisfy the relation ,,    a_ij = a_ji 
• _{Skew-symmetric matrix A matrix which satisfy the relationship ,,,} a_ij = -a_ji
• _{Triangular matrix A matrix whose elements below or above the leading diagonal are zero are called triangular matrix.}
• _{Transpose of a matrix A matrix obtained after exchanging the rows and columns of a matrix is called transpose of a matrix. It is donated as} A^T
• Orthogonal matrix A matrix which satisfy this relationship,,,,, A^T.A= 1
• Conjugate Matrix A matrix obtained by the complex conjugate of a matrix A is called Conjugate matrix. 

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