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Matrix=[[e^t,e^-t(sint-2cost),e^-t(-2sin...

Matrix`=[[e^t,e^-t(sint-2cost),e^-t(-2sint-cost)],[e^t,-e^-t(2sint+cost),e^-t(sint-2cost)],[e^t,e^tcost,e^-tsint]]` is invertible. (a) only if `t=(pi)/(2)` (b) only `t=pi` (c) `tepsilonR` (d) `t!inR`

A

Invertible only when `t=pi`

B

Invertible for every `t in R`

C

Not invertible for any `t in R `

D

Invertible only when `t=pi/2`

Text Solution

Verified by Experts

The correct Answer is:
B
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VMC MODULES ENGLISH-MATRICES AND DETERMINANTS -JEE MAIN ARCHIVE
  1. |(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b)|

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  2. Let a(1),a(2),a(3), …, a(10) be in G.P. with a(i) gt 0 for i=1, 2, …, ...

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  3. Let A=[(2,b,1),(b,b^(2)+1,b),(1,b,2)] where b gt 0. Then the minimum v...

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  4. Let d in R, and A[{:(,-2,4+d,(sin theta-2)),(,1,(sin theta)+2,d),(,5,(...

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  5. If B = [{:(5, 2alpha, 1),(0, 2, 1),(alpha, 3, -1):}] is the inver...

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  6. Matrix=[[e^t,e^-t(sint-2cost),e^-t(-2sint-cost)],[e^t,-e^-t(2sint+cost...

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  7. Let A and B be two invertible matrices of order 3xx3. If det. (ABA^(T)...

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  8. If A = [(costheta,-sintheta),(sintheta,costheta)], then the matrix A^(...

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  9. If [x] denotes the greatest integer le x, then the system of liner equ...

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  10. Let lambda be a real number for which the system of linear equations ...

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  11. If the system of linear equation x+y+z=5, x+2y+2z = 6, x+3y + lambda z...

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  12. If the system of equations, 2x + 3y-z = 0, x + ky -2z = 0 " and " 2x-y...

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  13. If the system of linear equations x-2y + kz = 1, 2x + y+ z = 2, 3x-y...

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  14. The greatest value of for which the system of linear equations x-c...

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  15. The set of all values of lambda for which the system of linear equatio...

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  16. An ordered pair (alpha, beta) for which the system of linear equations...

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  17. If the system of linear equations 2x+2y+3z=a 3x-y+5z=b x-3y+2z=...

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  18. The number of possible value of theta lies in (0,pi), such that system...

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  19. If the system of linear equations x-4y+7z=g, 3y-5z=h, -2x+5y-9z=k is c...

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  20. The system of linear equations x + y + z = 2 2x + 3y + 2z = 5 2...

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