2. Consider the following matrix sin³a sinB sin³y A cos a cos²B cos² a where a >3>7>0 are real numbers. Determine ||A||1-

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Q: 2. Show that for any x, the matrix A = A² = I. [cos(2x) sin(2x) [sin(2x) − cos(2x)] - satisfies the…

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Q: Evaluate [sin³ a x cos x dx. + C

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Q: trace the equation in 3 -dimension

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Q: Give the coordinates of the harmonic conjugate of (–1, –1, 0) with respect to (1, 1, 1) and (3, 3,…

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Q: fsin²7x dx Select one: O a. O b. O c. O d. O e. 7x - sin²7x cos 7x 14 7x sin7x cos 7x 7 7x + sin7x…

A: Formula used

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Q: Show that sin 3x and cos 3x are orthogonal on [−π, π].

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Q: If z = 1+ 2i and w 3+ 4i, express in rectangular form 5 cos [Arg (2²)] + 5i sin[Arg w]

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Q: Show that the matrix is invertible and find its inverse. 9] A-1 = A = sin 8 [₁ cos Ꮎ -cos 0 sin 0

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Q: (2) Find all the numbers z such that elz = 10i.

A: Consider the given. eiz=10i

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Q: EXER 7: MATRICES Prove that if N is invertible then MN¹ = N¹M if and only if MN=NM.

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Q: = cos 4 + isin and B = cos + i sin. Prove that B is not in Q(a).

A: Given: α=cos 2π7+i sin 2π7; β=cos 2π5+i sin 2π5To prove: β is not in Qα.

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Q: Prove that i2-i0 e-e %3D sincd

A: We have to prove eiθ-e-iθsin θ=2i Now, sin x can be expressed in exponential form as sin…

Q: (ii) Prove that the product of matrices cos²0 Icos@sin0 cos@sin@] sin?e cos²p B = lcosøsing…

A: Given the matrix is A=cos2θcosθsinθcosθsinθsin2θB=cos2φcosφsinφcosφsinφsin2φ

Q: Q5: Show that S 2T Cos 30 5-4 cose 11 ㅠ 12

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Q: Find differential o perator theit annihilates 4e cos3x+3x2e

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Q: EXER 13.2 a b Assuming that for matrix G d e h [9 we have det G= -7. Then find the ff: a. det(3G) b.…

A: WE WILL APPLY THE PROPERTY OF DETERMINANT TO FIND ANSWERS.

Q: Find the g.c.d. in Z [i] of 2 and 3+ 5i.

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