Matrices and Determinants 2 Question 17

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19. The parameter on which the value of the determinant 1aa2 cos(pd)xcospxcos(p+d)x

======= ####19. The parameter on which the value of the determinant

3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed

|1aa2cos(pd)xcospxcos(p+d)xsin(pd)xsinpxsin(p+d)x|

does not depend upon, is

(1997, 2M)

(a) a

(b) p

(c) d

(d) x

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Answer:

Correct Answer: 19. (b)

Solution:

  1. Let Δ= |1aa2cos(pd)xcospxcos(p+d)xsin(pd)xsinpxsin(p+d)x|

Applying C1C1+C3

Δ=|1+a2aa2cos(pd)x+cos(p+d)xcospxcos(p+d)xsin(pd)x+sin(p+d)xsinpxsin(p+d)x|

Δ=|1+a2aa22cospxcosdxcospxcos(p+d)x2sinpxcosdxsinpxsin(p+d)x|

Applying C1C12cosdxC2

Δ=|1+a22acosdxaa20cospxcos(p+d)x0sinpxsin(p+d)x|

Δ=(1+a22acosdx)[sin(p+d)xcospxsinpxcos(p+d)x]

Δ=(1+a22acosdx)sindx

which is independent of p.



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