COMEDK2016MathematicsMatrices
If O(A)=2 3, O(B)=3 2 , and O(C)=3 3 , which one of the following is not defined?
Options
- AC (A+B^ )
- BC (A+B^ )^
- CB A C
- DC B+A^
Correct answer
A. C (A+B^ )
Step-by-step solution
Given that, aligned O(A) &=2 3, O(B)=3 2 O(C) &=3 3 O (A^ ) &=3 2, O (B^ )=2 3 (a) C (A+B^ ) aligned Now, O (A+B^ )=2 3 and O(C)=3 3 So, matrix C (A+B^ ) cannot be determined. (b) C (A+B^ )^ O (A+B^ )=2 3 O (A+B^ )^ =3 2 and O(C)=3 3 Therefore, matrix C (A+B^ )^ can be determined. (c) O(B A)=3 3 and O(C)=3 3 Therefore, matrix B A C can be determined. (d) C B+A^ Now, order of C B=( order of C ) (order of B ) =( order of C is 3 3 ) (order of B is 3 2 ) = order of C B is 3 2 Since, O (A^ )=3 2 Therefore, matrix C B+A^