Respuesta :
Answer:
(a) Order of matrix B is 7 × 1 and order of matrix AB is 4 × 1.
(b) Order of matrix A is 5 × 5.
(c) The order of matrix B is 5 × 7.
Step-by-step explanation:
The product of two matrices is possible if and only if column of first matrix is equal to row of second matrix.
If A is an n × m matrix and B is an m × o matrix, their matrix product AB is an n × p matrix,
(a)
It is given that order of matrix A is 4 x 7.
B is a column matrix. It means the number of column in matrix B is 1.
Let the order of matrix B = n × 1
Product of matrices A and B is possible if and only if column of matrix A is equal to row of matrix B.
[tex]n=7[/tex]
Order of matrix B is 7 × 1
[tex]A_{4\times 7}B_{7\times 1}=AB_{4\times 1}[/tex]
Order of matrix AB is 4 × 1.
(b)
Order of matrix B = 5 × 5
It is given that A is the identity matrix.
Identity matrix is a square matrix having 1s on the main diagonal, and 0s everywhere else.
So, order of matrix A is equal to order of matrix B.
Order of matrix A = 5 × 5
Therefore order of matrix A is 5 × 5.
(c)
Order of matrix A = 4 × 5
Order of matrix AB = 4 × 7
Let Order of matrix B = n × m
[tex]A_{4\times 5}B_{n\times m}=AB_{4\times 7}[/tex]
Product of A and B are possible if and only if n=5.
[tex]A_{4\times 5}B_{5\times m}=AB_{4\times 7}[/tex]
[tex]AB_{4\times m}=AB_{4\times 7}[/tex]
On comparing both sides, we get
[tex]m=7[/tex]
Therefore the order of matrix B is 5 × 7.
