Matrices(11th And 12th > Mathematics ) Questions and Answers
Explanation:-
Answer: Option C. -> A+B′:
C
We can see from the options that if we take transpose of B,
B′ will be of 2 x 3 matrix which cannot be added to a 3 x 3 matrix, as for the addition the order should be the same.
Explanation:-
Answer: Option C. -> ⎡⎢⎣an000bn000cn⎤⎥⎦:
C
Since A2=A.A=⎡⎢⎣a000b000c⎤⎥⎦⎡⎢⎣a000b000c⎤⎥⎦=⎡⎢⎣a2000b2000c2⎤⎥⎦
And A3=⎡⎢⎣a3000b3000c3⎤⎥⎦,....⇒An=An−1.A=⎡⎢⎣an−1000bn−1000cn−1⎤⎥⎦⎡⎢⎣a000b000c⎤⎥⎦=⎡⎢⎣an000bn000cn⎤⎥⎦.
Note: Students should remember this question as a formula.
Explanation:-
Answer: Option A. -> Both A−1B and A−1B−1 are symmetric:
A
AB =BA
Previous & past multiplying both sides by A−1.
A−1(AB)A−1=A−1(BA)A−1(A−1A)(BA−1)=A−1B(AA−1)⇒(BA−1)1=(A−1B)1=(A−1)1B1(reversal laws)=A−1B(as B=B1)(A−1)1=A−1⇒A−1B is symmetric
Similarly for A−1B−1.