Understand multiplication of matrices. Click on the Link to Watch the VIDEO explanation:
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Multiplications Of Matrices - Numerical
Let us solve the numerical on multiplication of matrices.
Problem:
If P = matrix 5 2 2 1 and Q = 1 0 0 1 find PQ.
Let us see if the two matrices P and Q are multipliable the condition for multiplying two matrices is. two matrices A and B can be multiplied if the number of columns of A = number of rows of B. The resulted matrix will be of the order number of rows A = number of columns of B . i.e. if A be a matrix of order m by n and b be a matrix of order n by q. then A and B can be multiplied and there product will be a matrix of order m by q.
Here, in this example matrix B is of the order 2 by 2 and the matrix Q is of the order 2 by 2 so they can multiplied since the no. of columns in matrix B is equal the no. of rows in matrix Q i.e. 2.
Therefore the order of matrix PQ will be 2 by 2. Now let us understand how to multiply the matrix P and matrix Q. Matrices P and Q can be multiplied by using the row column multiplication technique as illustrated below:
Multiply the first row first column element of matrix P with a first row first column element of matrix Q then multiply the first row second column element of matrix P with the second row first column element of matrix Q in the matrix PQ you have now got 5*1 + 2*0 this will be first row first column element of matrix PQ continue the process to get the remaining element of the matrix PQ. Thus, we get PQ = matrix is 5 2 2 1 which is of the order 2 by 2. Now that matrix PQ = matrix P.
Hence matrix Q is an identity matrix we called a definition of the identity matrix a square matrix in which every diagonal element is 1 and every non diagonal element is 0 is called an identity or unit matrix and the property of an identity matrix is when a matrix is multiplied by an identity matrix we get the same matrix i.e. A*I = A = I*A.
Click on the exercise button at the bottom right of your screen and solve the problem.
Watch Video
Multiplications Of Matrices - Numerical
Let us solve the numerical on multiplication of matrices.
Problem:
If P = matrix 5 2 2 1 and Q = 1 0 0 1 find PQ.
Let us see if the two matrices P and Q are multipliable the condition for multiplying two matrices is. two matrices A and B can be multiplied if the number of columns of A = number of rows of B. The resulted matrix will be of the order number of rows A = number of columns of B . i.e. if A be a matrix of order m by n and b be a matrix of order n by q. then A and B can be multiplied and there product will be a matrix of order m by q.
Here, in this example matrix B is of the order 2 by 2 and the matrix Q is of the order 2 by 2 so they can multiplied since the no. of columns in matrix B is equal the no. of rows in matrix Q i.e. 2.
Therefore the order of matrix PQ will be 2 by 2. Now let us understand how to multiply the matrix P and matrix Q. Matrices P and Q can be multiplied by using the row column multiplication technique as illustrated below:
Multiply the first row first column element of matrix P with a first row first column element of matrix Q then multiply the first row second column element of matrix P with the second row first column element of matrix Q in the matrix PQ you have now got 5*1 + 2*0 this will be first row first column element of matrix PQ continue the process to get the remaining element of the matrix PQ. Thus, we get PQ = matrix is 5 2 2 1 which is of the order 2 by 2. Now that matrix PQ = matrix P.
Hence matrix Q is an identity matrix we called a definition of the identity matrix a square matrix in which every diagonal element is 1 and every non diagonal element is 0 is called an identity or unit matrix and the property of an identity matrix is when a matrix is multiplied by an identity matrix we get the same matrix i.e. A*I = A = I*A.
Click on the exercise button at the bottom right of your screen and solve the problem.
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