1.

For x>0, define A=⎡⎢⎢⎢⎣x+1x000x00016⎤⎥⎥⎥⎦, B=⎡⎢⎢⎢⎢⎢⎢⎢⎣5xx2+10003x00014⎤⎥⎥⎥⎥⎥⎥⎥⎦ Let X=(AB)−1+(AB)−2+⋯+(AB)−nY=limn→∞XZ=Y−1−2I where I is an identity matrix of order 3. Column I Column II (A) The minimum value of [ trace (AY) ] is{[.] represents the greatest integer function} (P) 24(B) The value of det(Y−1) is(Q) 12(C) If trace (Z+Z2+Z3+⋯+Z10)=2a+b(a,b∈N), then a+b is equal to(R) 6(D) If |adj(√5Y−1)|=k, then the number of odd positive divisors of k is (S) 19 Note: Trace of a square matrix is the sum of the diagonal elements. Which of the following is the CORRECT combination?

Answer»

For x>0, define
A=⎡⎢
⎢
⎢⎣x+1x000x00016⎤⎥
⎥
⎥⎦,

B=⎡⎢
⎢
⎢
⎢
⎢
⎢
⎢⎣5xx2+10003x00014⎤⎥
⎥
⎥
⎥
⎥
⎥
⎥⎦

Let X=(AB)−1+(AB)−2+⋯+(AB)−nY=limn→∞XZ=Y−1−2I
where I is an identity matrix of order 3.

Column I Column II (A) The minimum value of [ trace (AY) ] is{[.] represents the greatest integer function} (P) 24(B) The value of det(Y−1) is(Q) 12(C) If trace (Z+Z2+Z3+⋯+Z10)=2a+b(a,b∈N), then a+b is equal to(R) 6(D) If |adj(√5Y−1)|=k, then the number of odd positive divisors of k is (S) 19


Note: Trace of a square matrix is the sum of the diagonal elements.

Which of the following is the CORRECT combination?


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