The set S = { 1, sin(x), cos(x) } is : Select one: O a. orthonormal O b. Dependent O c. Basis for R3 O d. Orthogonal

Q: Are x, sin(x) and cox(x) linearly independent

A: True x, sin(x), cos(x) are linearly independent

Q: Find the coordinate vector of x = basis B [X] B = = M 4 LOJ of R³. 0 {Q.48} [B] with respect to the

A: The coordinate vector of x with respect to basis B={v1,v2,⋯,vn} is [x]B=[a1a2⋮an] such that…

Q: Show that the operator U is positive U: 1² ([0,1]) → L²([0,1]), Uƒ (x) = X[{0,1] [~*\f(t)\dt

A: To show that the operator U is positive, need to demonstrate that for any f∈L2([0,1]), the inner…

Q: Find the vectors T and N and the binormal vector B = T x N, for the vector-valued function r(t) at…

A: Given, the vector-valued function  to find:  the vectors  and  and the binomial vector  at .

Q: 7. What basis for V = M(n, R) does Theorem 3.3 i) yield when applied to T(A) = A + AT, with W M(n,…

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Q: Q5 Let et A = cost) -sint) sin (t) cos (t) ehow that A ;es Invertible, Find AI using the cotactere…

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Q: (A+B)* = A† + B*, (AB)† = B* A*, (AA)† = XA*, %3D %3D where A is a complex number and AŤ indicates…

A: We have to evaluate ABC†. Given AB†=B†A† Hence, ABC†=ABC†=C†AB†USe AB†=B†A†=C†B†A†=C†B†A†

Q: Let 9 be the function defined by g(z) = = z² +i (a) Calculate the modulus and principal argument of…

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Q: ? Exercise 14.5.2 дz Az To calculate and for the following functions: Ju дv first calculate: Oz Ax…

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Q: Prove the following vector identity using index notation: A × (B × C) = (A · C)B — (A · B)C.

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Q: dr = wa x b dt r X

A:

Q: The linear transform T: V1 → V2 plots the base vectors j and i as follows: T(i) = i +j , TG) = 2i –…

A: The Linear transformation is given by T : V1 →V2T(i)=i+jT(j)=2i-j where I and j are basis vectors.

Q: Compute the Jacobian at the indicated point. G(r, t) = (r sin (t), r — cos (t)), (r, t) = =(5,2)…

A: Jacobian of the function