If A, B and C are three matrices of order 2 × 3, 3 × 2 and 3 × 3, then the matrices given in which of the following options are defined?
- A)
A + B, A + BT, (AB) T
- B)
(AB) T, ACBT, A B
- Next
- clear
ACBT, AC + BT, AB
4C, ACBT, CTB + A
the order of the matrix A is 2*3
the order of matrix B is 3*2
the order of matrix C is 3*3
since the order of the matrix A and B are not same.
therefore A+B is not defined.
thus option (a) is wrong
the number of columns in matrix A is equal to the number of rows in matrix B.
thus AB is defined and transpose of AB is also defined.
the number of columns in matrix A is equal to the number of rows in matrix C.
thus AC is defined ad order of AC is 2*3
the order of transpose of B is 2*3.
since the number of columns in matrix AC is not equal to number of rows in transpose of matrix B.
thus is not defined and option (b) is wrong
from the above is not defined thus option (c) is wrong.
the order of AC and is same . thus the sum is defined. thus is defined.
hope this helps you
the order of matrix B is 3*2
the order of matrix C is 3*3
since the order of the matrix A and B are not same.
therefore A+B is not defined.
thus option (a) is wrong
the number of columns in matrix A is equal to the number of rows in matrix B.
thus AB is defined and transpose of AB is also defined.
the number of columns in matrix A is equal to the number of rows in matrix C.
thus AC is defined ad order of AC is 2*3
the order of transpose of B is 2*3.
since the number of columns in matrix AC is not equal to number of rows in transpose of matrix B.
thus is not defined and option (b) is wrong
from the above is not defined thus option (c) is wrong.
the order of AC and is same . thus the sum is defined. thus is defined.
hope this helps you