PPT: Basics of Matrix & Operations on Matrix

PPT: Basics of Matrix & Operations on Matrix | Engineering Mathematics - Civil Engineering (CE) PDF Download

``` Page 1

4.4 Matrices: Basic Operations
Page 2

4.4 Matrices: Basic Operations
? To add or subtract matrices, they must be of the same order,
corresponding entries.  To subtract matrices of the same order,
subtract their corresponding entries. The general rule is as
follows using mathematical notation:
ij ij
ij ij
A B a b
A B a b
??
? ? ?
??
??
? ? ?
??
Page 3

4.4 Matrices: Basic Operations
? To add or subtract matrices, they must be of the same order,
corresponding entries.  To subtract matrices of the same order,
subtract their corresponding entries. The general rule is as
follows using mathematical notation:
ij ij
ij ij
A B a b
A B a b
??
? ? ?
??
??
? ? ?
??
An example:
? First, note that each matrix
has dimensions of 3X3, so
we are able to perform the
at right:
corresponding entries we
have
4 3 1 1 2 3
0 5 2 6 7 9
5 6 0 0 4 8
??
? ? ? ?
? ? ? ?
? ? ?
? ? ? ?
? ? ? ?
??
? ? ? ?
3 1 4
6 2 7
5 10 8
?
??
??
?
??
??
?
??
Page 4

4.4 Matrices: Basic Operations
? To add or subtract matrices, they must be of the same order,
corresponding entries.  To subtract matrices of the same order,
subtract their corresponding entries. The general rule is as
follows using mathematical notation:
ij ij
ij ij
A B a b
A B a b
??
? ? ?
??
??
? ? ?
??
An example:
? First, note that each matrix
has dimensions of 3X3, so
we are able to perform the
at right:
corresponding entries we
have
4 3 1 1 2 3
0 5 2 6 7 9
5 6 0 0 4 8
??
? ? ? ?
? ? ? ?
? ? ?
? ? ? ?
? ? ? ?
??
? ? ? ?
3 1 4
6 2 7
5 10 8
?
??
??
?
??
??
?
??
Subtraction of matrices
? Now, we will subtract
the same two matrices
? Subtract corresponding
entries as follows:
4 3 1 1 2 3
0 5 2 6 7 9
5 6 0 0 4 8
??
? ? ? ?
? ? ? ?
? ? ?
? ? ? ?
? ? ? ?
??
? ? ? ?
4 ( 1) 3 2 1 3
0 6 5 ( 7) 2 9
5 0 6 ( 4) 0 8
? ? ? ? ?
??
??
? ? ? ? ?
??
?? ? ? ? ? ?
??
5 5 2
6 12 11
5 2 8
??
??
??
??
??
??
??
??
=
Page 5

4.4 Matrices: Basic Operations
? To add or subtract matrices, they must be of the same order,
corresponding entries.  To subtract matrices of the same order,
subtract their corresponding entries. The general rule is as
follows using mathematical notation:
ij ij
ij ij
A B a b
A B a b
??
? ? ?
??
??
? ? ?
??
An example:
? First, note that each matrix
has dimensions of 3X3, so
we are able to perform the
at right:
corresponding entries we
have
4 3 1 1 2 3
0 5 2 6 7 9
5 6 0 0 4 8
??
? ? ? ?
? ? ? ?
? ? ?
? ? ? ?
? ? ? ?
??
? ? ? ?
3 1 4
6 2 7
5 10 8
?
??
??
?
??
??
?
??
Subtraction of matrices
? Now, we will subtract
the same two matrices
? Subtract corresponding
entries as follows:
4 3 1 1 2 3
0 5 2 6 7 9
5 6 0 0 4 8
??
? ? ? ?
? ? ? ?
? ? ?
? ? ? ?
? ? ? ?
??
? ? ? ?
4 ( 1) 3 2 1 3
0 6 5 ( 7) 2 9
5 0 6 ( 4) 0 8
? ? ? ? ?
??
??
? ? ? ? ?
??
?? ? ? ? ? ?
??
5 5 2
6 12 11
5 2 8
??
??
??
??
??
??
??
??
=
Scalar Multiplication
? The scalar product of a number k and a
matrix A is the matrix denoted by kA,
obtained by multiplying each entry of A by
the number k . The number k is called a
scalar. In mathematical notation,
ij
A k ka
??
?
??
```

Engineering Mathematics

65 videos|120 docs|94 tests

FAQs on PPT: Basics of Matrix & Operations on Matrix - Engineering Mathematics - Civil Engineering (CE)

 1. What is a matrix and how is it represented?
Ans. A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns. It is typically represented using brackets or parentheses. For example, a matrix A with m rows and n columns can be written as A = [a_ij], where a_ij represents the element in the i-th row and j-th column.
 2. What are the basic operations that can be performed on matrices?
Ans. There are several basic operations that can be performed on matrices, including addition, subtraction, and multiplication. Matrix addition is performed by adding corresponding elements of two matrices, while matrix subtraction is done by subtracting corresponding elements. Matrix multiplication involves multiplying the elements of one matrix with the elements of another matrix according to specific rules.
 3. How is matrix multiplication different from scalar multiplication?
Ans. Matrix multiplication is different from scalar multiplication because it involves multiplying corresponding elements of two matrices to obtain a new matrix, while scalar multiplication involves multiplying each element of a matrix by a scalar (a single number). In matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix, whereas scalar multiplication can be performed on any matrix.
 4. Can matrices be divided like numbers?
Ans. No, matrices cannot be divided like numbers. Division of matrices is not a defined operation. While matrix multiplication is possible, division is not a direct operation on matrices. However, there are certain cases where matrix division-like operations, such as finding the inverse of a matrix, can be performed.
 5. What is the identity matrix and how is it related to matrix operations?
Ans. The identity matrix is a special square matrix where all the elements on the main diagonal are 1 and all other elements are 0. It is denoted as I. When a matrix is multiplied by the identity matrix, the original matrix remains unchanged. This property is similar to multiplying a number by 1, which results in the number itself. The identity matrix plays an important role in various matrix operations, such as finding the inverse of a matrix or solving systems of linear equations.

Engineering Mathematics

65 videos|120 docs|94 tests

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