Flashcards: Matrices

``` Page 1

MATRICES
A set of ???? numbers (real or complex) arranged in the form of a rectangular array having ' ?? ' rows and '
?? ' columns is called an ?? × ?? matrix. It is usually written as
?? = [
?? 11
?? 12
? ?? 1?? ?? 21
?? 22
? ?? 2?? ? ? ? ?
?? ?? 1
?? ?? 2
? ?? ????
]

Page 2

MATRICES
A set of ???? numbers (real or complex) arranged in the form of a rectangular array having ' ?? ' rows and '
?? ' columns is called an ?? × ?? matrix. It is usually written as
?? = [
?? 11
?? 12
? ?? 1?? ?? 21
?? 22
? ?? 2?? ? ? ? ?
?? ?? 1
?? ?? 2
? ?? ????
]

MATRICES
It is represented as ?? = [?? ????
]
?? ×?? . The numbers ?? 11
,?? 12
,… etc. are called elements of the matrix. The
element ?? ????
belong to ?? th
row and ?? th
column.
e.g., ?? = [
3 2 7
5 -4 6
4 8 -12
] is a 3 × 3 matrix

Page 3

MATRICES
A set of ???? numbers (real or complex) arranged in the form of a rectangular array having ' ?? ' rows and '
?? ' columns is called an ?? × ?? matrix. It is usually written as
?? = [
?? 11
?? 12
? ?? 1?? ?? 21
?? 22
? ?? 2?? ? ? ? ?
?? ?? 1
?? ?? 2
? ?? ????
]

MATRICES
It is represented as ?? = [?? ????
]
?? ×?? . The numbers ?? 11
,?? 12
,… etc. are called elements of the matrix. The
element ?? ????
belong to ?? th
row and ?? th
column.
e.g., ?? = [
3 2 7
5 -4 6
4 8 -12
] is a 3 × 3 matrix

TYPES OF MATRICES
1 Square Matrix : A matrix having equal number of rows and columns is called a square matrix.
If the matrix ?? has ?? rows and ?? columns, it is said to be square matrix of order ?? .
Example : [
1 2 3
2 3 4
3 4 5
] is a square matrix of order 3.
The diagonal of this matrix containing the elements 1,3,5 is called the leading or principal diagonal.
Trace of matrix : The sum of the diagonal elements of a square matrix ?? is called trace of ?? .
Trace? (?? ) = ?
?? =1
?? ??? ????

Page 4

MATRICES
A set of ???? numbers (real or complex) arranged in the form of a rectangular array having ' ?? ' rows and '
?? ' columns is called an ?? × ?? matrix. It is usually written as
?? = [
?? 11
?? 12
? ?? 1?? ?? 21
?? 22
? ?? 2?? ? ? ? ?
?? ?? 1
?? ?? 2
? ?? ????
]

MATRICES
It is represented as ?? = [?? ????
]
?? ×?? . The numbers ?? 11
,?? 12
,… etc. are called elements of the matrix. The
element ?? ????
belong to ?? th
row and ?? th
column.
e.g., ?? = [
3 2 7
5 -4 6
4 8 -12
] is a 3 × 3 matrix

TYPES OF MATRICES
1 Square Matrix : A matrix having equal number of rows and columns is called a square matrix.
If the matrix ?? has ?? rows and ?? columns, it is said to be square matrix of order ?? .
Example : [
1 2 3
2 3 4
3 4 5
] is a square matrix of order 3.
The diagonal of this matrix containing the elements 1,3,5 is called the leading or principal diagonal.
Trace of matrix : The sum of the diagonal elements of a square matrix ?? is called trace of ?? .
Trace? (?? ) = ?
?? =1
?? ??? ????

2 Diagonal Matrix : A square matrix in which all the elements, except those in the leading
diagonal are zero is called a diagonal matrix. Thus square matrix is called diagonal matrix if ?? ????
= 0
for ?? ? ?? .
e.g., ?? = [
2 0 0
0 1 0
0 0 4
] or [
?? 1
0 0
0 ?? 2
0
0 0 ?? 3
]
Above are diagonal matrices of the type 3 × 3. These are in short written as diag? [2,1,4] or diag
[?? 1
,?? 2
,?? 3
]
If the diagonal elements are ?? 1
,?? 2
,…?? ?? , then it is written as diag? [?? 1
,?? 2
,… ,?? ?? ].

Page 5

MATRICES
A set of ???? numbers (real or complex) arranged in the form of a rectangular array having ' ?? ' rows and '
?? ' columns is called an ?? × ?? matrix. It is usually written as
?? = [
?? 11
?? 12
? ?? 1?? ?? 21
?? 22
? ?? 2?? ? ? ? ?
?? ?? 1
?? ?? 2
? ?? ????
]

MATRICES
It is represented as ?? = [?? ????
]
?? ×?? . The numbers ?? 11
,?? 12
,… etc. are called elements of the matrix. The
element ?? ????
belong to ?? th
row and ?? th
column.
e.g., ?? = [
3 2 7
5 -4 6
4 8 -12
] is a 3 × 3 matrix

TYPES OF MATRICES
1 Square Matrix : A matrix having equal number of rows and columns is called a square matrix.
If the matrix ?? has ?? rows and ?? columns, it is said to be square matrix of order ?? .
Example : [
1 2 3
2 3 4
3 4 5
] is a square matrix of order 3.
The diagonal of this matrix containing the elements 1,3,5 is called the leading or principal diagonal.
Trace of matrix : The sum of the diagonal elements of a square matrix ?? is called trace of ?? .
Trace? (?? ) = ?
?? =1
?? ??? ????

2 Diagonal Matrix : A square matrix in which all the elements, except those in the leading
diagonal are zero is called a diagonal matrix. Thus square matrix is called diagonal matrix if ?? ????
= 0
for ?? ? ?? .
e.g., ?? = [
2 0 0
0 1 0
0 0 4
] or [
?? 1
0 0
0 ?? 2
0
0 0 ?? 3
]
Above are diagonal matrices of the type 3 × 3. These are in short written as diag? [2,1,4] or diag
[?? 1
,?? 2
,?? 3
]
If the diagonal elements are ?? 1
,?? 2
,…?? ?? , then it is written as diag? [?? 1
,?? 2
,… ,?? ?? ].

3 Scalar Matrix : A diagonal matrix in which all the elements in the leading diagonal are equal is
called scalar matrix. It is equal to ?? ?? ?? for some scalar ?? .
e.g., ?? = [
3 0 0
0 3 0
0 0 3
] or [
?? 0 0
0 ?? 0
0 0 ?? ]
In general for a scalar matrix, ?? ????
= 0 for ?? ? ?? and ?? ????
= ?? for ?? = ?? .

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Mathematics (Maths) for JEE Main & Advanced

209 videos|443 docs|143 tests

FAQs on Flashcards: Matrices - Mathematics (Maths) for JEE Main & Advanced

 1. What are matrices in mathematics?
Ans. Matrices are rectangular arrays of numbers, symbols, or expressions arranged in rows and columns. They are used to represent data or perform mathematical operations.
 2. How are matrices added and subtracted?
Ans. Matrices can be added or subtracted by simply adding or subtracting corresponding elements. The matrices must have the same dimensions for addition or subtraction to be possible.
 3. What is the identity matrix?
Ans. The identity matrix is a square matrix in which all the elements of the main diagonal are 1, and all other elements are 0. It acts as a neutral element for matrix multiplication.
 4. How do you multiply matrices?
Ans. To multiply two matrices, the number of columns in the first matrix must equal the number of rows in the second matrix. The product matrix is obtained by multiplying corresponding elements and summing them up.
 5. What is the determinant of a matrix?
Ans. The determinant of a square matrix is a scalar value that can be calculated from its elements. It is used to determine if a matrix has an inverse and plays a crucial role in solving systems of linear equations.

Mathematics (Maths) for JEE Main & Advanced

209 videos|443 docs|143 tests

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