Introduction to Multiplication of 2by 2 Matrix:
There are two types of multiplications is there.
Scalar multiplication
Matrix Multiplication
Scalar multiplication:
It is an ordinary multiplication.the regular numbers are called the scalar.
Matrix multiplication:
It is the operation of multiplying a matrix with another matris or multiplying matrix with scalar.
Ordinary matrix product:
It is mostly used to Multiplying Matrices. The multiplication is defined between two matrices If only the breadth of the first matrix is equals to the height of the next matrix that means the second matrix.
If we multiplying mx a matrix with aXn matrix means the result will be the m x n matrix..
Properties of Matrix Multiplication:
Properties of matrix multiplication:
It is not usually commutative. that means AB BA.
If A and B are the two n x n matrices , then the determinant of its product is independent for the order of the matrices in their products.
If both the matrices are diagonal matrices then their product is commutative.
The matrix multiplication is satisfies the Associative property.
A(BC)=(AB)C
It is distributive over the addition:
A(B+C)=AB+AC
(A+B)C=AC+BC
It is compatible with the scalar multiplication.
It does not satisfied the commutative property.
How to multiply matrices
Consider two matrices A and B .
step 1:The first row first element of the matrix A is multiply by the First column First element of the matrix B.
step 2: And add to the The first row second element of the matrix A is multiply by the first column second element of the matrix B.
Step 3:The second row first element of the matrix A is multiply by the second column First element of the matrix B.
step 4: And add to the second row second element of the matrix A is multiply by the second column second element of the matrix B.
My forthcoming post is on what is the algebraic expression, algebra solver step by step free will give you more understanding about Algebra.
Example for 2 X 2 Matrix Multiplication
Example for 2 x 2 matrix multiplication
Ex 1 : `[[2,3],[1,3]]` `xx``[[0,1],[2,1]]`
Sol : Step 1:
(2 3 )`((0),(2))`
= (2 x 0)+(3 x2)
=6
Step 2: (2 3)`((1),(1))`
=(2 `xx` 1)+ (3`xx`
=2+3
=5
Like wise we have to do the remaining steps.
= `[[6,5],[6,4]]`
There are two types of multiplications is there.
Scalar multiplication
Matrix Multiplication
Scalar multiplication:
It is an ordinary multiplication.the regular numbers are called the scalar.
Matrix multiplication:
It is the operation of multiplying a matrix with another matris or multiplying matrix with scalar.
Ordinary matrix product:
It is mostly used to Multiplying Matrices. The multiplication is defined between two matrices If only the breadth of the first matrix is equals to the height of the next matrix that means the second matrix.
If we multiplying mx a matrix with aXn matrix means the result will be the m x n matrix..
Properties of Matrix Multiplication:
Properties of matrix multiplication:
It is not usually commutative. that means AB BA.
If A and B are the two n x n matrices , then the determinant of its product is independent for the order of the matrices in their products.
If both the matrices are diagonal matrices then their product is commutative.
The matrix multiplication is satisfies the Associative property.
A(BC)=(AB)C
It is distributive over the addition:
A(B+C)=AB+AC
(A+B)C=AC+BC
It is compatible with the scalar multiplication.
It does not satisfied the commutative property.
How to multiply matrices
Consider two matrices A and B .
step 1:The first row first element of the matrix A is multiply by the First column First element of the matrix B.
step 2: And add to the The first row second element of the matrix A is multiply by the first column second element of the matrix B.
Step 3:The second row first element of the matrix A is multiply by the second column First element of the matrix B.
step 4: And add to the second row second element of the matrix A is multiply by the second column second element of the matrix B.
My forthcoming post is on what is the algebraic expression, algebra solver step by step free will give you more understanding about Algebra.
Example for 2 X 2 Matrix Multiplication
Example for 2 x 2 matrix multiplication
Ex 1 : `[[2,3],[1,3]]` `xx``[[0,1],[2,1]]`
Sol : Step 1:
(2 3 )`((0),(2))`
= (2 x 0)+(3 x2)
=6
Step 2: (2 3)`((1),(1))`
=(2 `xx` 1)+ (3`xx`
=2+3
=5
Like wise we have to do the remaining steps.
= `[[6,5],[6,4]]`
