Q3 (3 points) Show that if both AB and B A are defined then AB and...
44. a.Let A and B be two 2 × 2 matrices,Let Tr denote the trace and det denote the determinant. Prove that Tr(AB)-Tr(BA) and det(AB) - det(BA). b. If A is any matrix in SLa(R), prove that det ((-A-t +1 where t = Tr(A). 44. a.Let A and B be two 2 × 2 matrices,Let Tr denote the trace and det denote the determinant. Prove that Tr(AB)-Tr(BA) and det(AB) - det(BA). b. If A is any matrix in SLa(R), prove...
ILI UU Q3 (8 points) Find general equation of the plane containing the following two lines C: y =24+1 t +3 5+2 and = 24 L : y = -2 25t-1 + Drag and drop your files or Click to browse Q4 (8 points) (a) Find parametric equations of the line passing through the point A(S. -2,9) and perpendicular to the plane 32 - y - 63 + 2 = 0. (b) Find two planes that intersect along the line...
immediate answers please Q3 (8 points) Given [ (2x² = x + 3) dx Question 3 parts a) and b) are worth a total of 8 marks. Drop your files in the appropriate box. There are NO FILES to drop here. + Drag and drop your files or click to browse... Q3a (0 points) a) Evaluate the integral using the definition. + Drag and drop your files or click to browse... Q3b (0 points) b) Evaluate the integral using the...
Q1 (4 points) Assume that f: NXN N is a function defined by f(n, k) = 2n+l(4k + 3). Is an injective function? Justify your answer. + Drag and drop your images or click to browse...
Q3 (6 points) Let T be the rotation (counterclockwise) of R2 by an angle ofLet S R2R2 be the reflection with respect to the line y 3 x. S and T are both linear transformations. (a) (4 points) Determine the standard matrix of S. Give details about how your obtained your answer. b) (1 point) Write down the standard matrix of T. Give only the answer, no justification needed. (c) (1 point) What is the standard matrix of S。TY Drag...
Please answer all parts with full, clear solutions so i can understand :) :) Q2 (6 points) If C is a smooth plane curve with parametrization r r(t),t E [a, b], then the curvature K(t) of C at the point r(t) is defined to be the magnitude of the rate of change -ll dT of the unit tangent vector with respect to the arc length. That is, = ds () [2p] Show that K(t) = ||F (C) xr" (t)|| r...
related to theory of automation. Thank you. 4) Minimize the number of states of the below DFA. (10 Points) q2 q1 1,0 q3 q4 q5 5-a) Find a NFA that accepts the following language: L-(aa" + aba*b*) (5 Points) b) Find an NFA that accepts the language L (aa (ab b)) (5 Points) 4) Minimize the number of states of the below DFA. (10 Points) q2 q1 1,0 q3 q4 q5 5-a) Find a NFA that accepts the following language:...
Find each of the matrices or explain why it is not defined: A+B; BA; AB, if А ſi 4 02 7] ſo 1 11 B = 1 -1 2 2 3 0
Please solve it in very detail, and make sure it is correct. C Max R Reux Belux C Ples x C Cel X CCM X CLS > Selux S SOLX Solix بل ادا 3 Solul X Mail * SCM X Post X + C .app.Acar.com/tudent/assessments/math-2203-770-limal-exam-2020 OM + Drag and drop your files or click to browse... th Q4 (8 points) My Courses By justifying your answer, determine whether the function T is a linear transformation. Linear Algebra II (MATH-2203-7... (a)...
(i) Show that a non-zero polynomial in ??[?]Zp[x] has exactly ?−1p−1 associates. (ii) Let ?R be a field, 0≠?(?),?(?)∈?[?]0≠a(x),b(x)∈R[x]. Prove that ?(?)a(x) ?(?)b(x) are associates of each other if and only if ?(?)∣?(?)a(x)∣b(x)and ?(?)∣?(?)b(x)∣a(x). Q5 (4 points) (i) Show that a non-zero polynomial in Zp[x] has exactly p - 1 associates. a(x), b(x) E R[x]. Prove that a(x) b(x) are associates of each other if and only if a(x) | b(x) (ii) Let R be a field, 0 and b(x)...