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By using properties of determinats. Prov...

By using properties of determinats. Prove that-
`|(sintheta,costheta,sin2theta),(sin(theta+(2pi)/3), cos(theta + (2pi)/3) ,sin(2theta + (4pi)/3)),(sin(theta-(2pi)/3) ,cos(theta - (2pi)/3), sin (2theta - (4pi)/3))|= 0`

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Prove that for all values of theta , |{:(sintheta,costheta,sin2theta),(sin(theta+(2pi)/(3)),cos(theta+(2pi)/(3)),sin(2theta+(4pi)/(3))),(sin(theta-(2pi)/(3)),cos(theta-(2pi)/(3)),sin(2theta-(4pi)/(3))):}|=0

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CENGAGE PUBLICATION-DETERMINANTS-All Questions
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  2. Let a ,b , c be the real numbers. The following system of equations in...

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  3. By using properties of determinats. Prove that- |(sintheta,costheta,...

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  5. let a > 0 , d > 0 find the value of the determinant |[1/a,1/(a(a + d))...

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  8. Prove that |[a x-b y-c z, a y+b x, c x+a z], [a y+b x, b y-c z-a x, b...

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  10. If alpha,beta,gamma are different from 1 and are the roots of a x^3+b ...

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  11. If p+q+r=0=a+b+c , then the value of the determinant |[p a, q b, r c],...

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  12. Let triangle =|[2a1b1, a1b2+a2b1, a1b3+a3b1], [a1b2+a2b1, 2a2b2, a2b3+...

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  13. If 2s=a+b+c and A=|[a^2,(s-a)^2,(s-a)^2],[(s-b)^2,b^2,(s-b)^2],[(s-c)^...

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  14. Find the value of lambda for which |{:(2a1+b1 , 2a2+b2 , 2a3+b3),(2b1+...

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  15. Prove that: |[-2a, a+b,a+c],[ b+a,-2b,b+c],[c+a, c+b,-2c]|=4(a+b)(b+c...

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  16. if a determinant of order 3xx 3 is formed by using the numbers 1 ...

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  17. If z=|[-5, 3+4i,5-7i],[3-4i,6 ,8+7i],[5+7i,8-7i,9]|,t h e nz is (a) p...

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  18. Consider the following linear equations: a x+b y+c z=0 b x+c y+a z=0 c...

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  19. Let omega be the complex number cos(2pi/3)+isin(2pi/3) Then the number...

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