Which one of the following matrices is orthonormal? A. B. sin 0 cos D. 2 4 -2 1 0 - cos 0 sin 0 C. None of these. - (0 ≤ R)

Q: Fill in the blank so that the following statement is true. 7 15x +9 %3D x+2 X+7 (x+2)(x + 7) 4 7 15x…

A: Given: The equation is 4x+2+7x+7=15x+9x+2x+7. The objective is to find the resulting equation of…

Q: cos (z) = e+1 eiz+e-iz 2i eiz+e¯iz e+e 2i

A:

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: Use Gauss-Jordan method to calculate the inverse of A A-l = |1 0 -1 A =| 0 1 1 1 1 1

A: By Gauss Jordan Elimination method the inverse of matrix is given as follows :

Q: Perform the indicated operation if possible. If not possible, enter "DNE": 4 2 -51 0 -10 51 5 -4 -9…

A:

Q: sin x COS X [ COS X - sin x

A: Answer and explanation is given below..

Q: x cos 2x e3¤ (e) - Va) [z (P) d [2

A: d/dx(uv) = vdu/dx + udv/dx  d/dx(u/v) =( vdu/dx - udv/dx )/ v^2  d/dx(u+v) = du/dx + dv/dx

Q: 1 1 √√x+2 dx. 貼 Evaluate O A. 39 O B. 38.0894 O C. 15.6291 O D. 6.5798

A: Since you have asked multiple questions so we will solve first question for you.

Q: Let X Beta(a, B) andY Beta distribution pdf: fx (x) = caª-1(1 – x)8–1 for x E (0, 1) and parameters…

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Q: 11 csc (7x) cot(7x) dæ : (Use Substitution Method) 11 11 + C 14 sin? (7x) 14 11 11 + C 14 cot2(7x)…

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Q: QuestionTO cos( z+ Da sin(e-2+ In(z)) + C 4 Ob. -4 sin(e-z+ In(z)) + C Oc. --- sin(e-z+ In(z)) + C 4…

A: Given query is to evaluate the integral.

Q: Suppose A= XAx-1. Take determinants to prove detA = detA = >.1>.2 ···An. This quick proof only…

A: Given: A=XΛX-1. Take determinants to prove detA=detΛ=λ1·λ2·. . . ·λn. To Fill in the blank: This…

Q: 1 Prove that sec 03D Cos 0

A: Let P(x,y) be a point on a circle of radius r associated with the angle θ.

Q: Show that if an = 3n3-17n2 + 2n-6, then an = Θ(n3).

A:

Q: 2/2 16/1+cos 0 de 0

A: We use the half-angle identity

Q: Solve the following Exact ODE

A: This is a problem of DE.

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: sec 0 + In +22+3 = -3 In y? + 32 -4 = 1+ cos 20 2/1+ (tan 0)2 + 2ln y + 2² =-3

A:

Q: Find cond1(A ) and cond∞(A). State whether th e given matrix is ill-conditioned.

A: To find:  and

Q: Evaluate the principal value of Cos ¹(-3+j).

A: Use the definition of the inverse of cosine function: y=cos-1x, then x=cosy, 0≤y≤π Now consider the…

Q: 1 1 | Let A = | 2 1 3 3 Find the cofactors A21, A22, A23. Find det(A).

A: The given matrix is A=11-1221313 The cofactor of an element is determined as; Cij=-1i+jMIj where i…

Q: If cos A + cos B = sin A cos B, then cos(A + B) =

A:

Q: Compute the Jacobian at the indicated point. G(r, t) = (r sin (t), r – cos (t)), (r, t) = ( 6,…

A: Jacobian of the function at a given point

Q: n Prove the "column j" expansion for the determinant: det A = (-1)¹¹¹ A¡¡ det áj. i=1

A: We have to prove following determinant formula for any matrix A with respect to "column j". det A =…

Q: 1. [3 pts. each] Let X and Y be 3 x 3 matrices such that det(X) = 3 and det(Y) = -7. Compute the…

A:

Q: Compute the determinants in using cofactor expansion along the first row and along the first column.

A: Consider a determinant: D=1-10-10101-1……1

Q: cos z = cos x cosh y– jsin x sinh y

A: Complex numbers

Q: 4 8. 5. Let C = 0. the cofactor matrix of a matrix A and let 7. -7 9] 611 b12 b13 A the inverse…

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Q: 5s Evaluate J|2 sin s Jdtds 0 0 I[ 2 OA. 3 (1 – sin(125)) O B. 3 (1+ sin(125)) (1+ cos(125)) 3 OC. 2…

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Q: If n = 15, X= 60, Y = 45, XY = 180 then the covariance Cov(X, Y) will be %3D Select one: O -1 O 11.2…

A: To find: Cov(X , Y) =??

Q: Decompose the fraction

A: To decompose the fractionsin2xcosx

Q: If n=15, EXY=180, EX=60, EY=45 then the covariance Cov(X, Y) will be Select one: O +1 O -1 O 11.2

A:

Q: Evaluate A2 (sin x) O A. sin(x + 2h) – sin(x + h) + 2 sin x O B. sin(x + h) – sin x O C. sin(x + 2h)…

A: We  need to evaluate ∆2(sinx) The solution is explained below.

Q: Show that if z = cos u + i sin u, then | z | =1

A: We have to show that if z=cos u+i sin u, then z=1. We know for any complex number if z=x+i y then…