(1 5 -4 Given the matrix A = 1-3 4 2 2 4 (a) Find the determinant of A. [4 marks] (b) Calculate the inverse of A. [8 marks] (c) Hence find the general solution of the linear simultaneous equations x+5y -4z -w = 3 x-3y +4z +w = 3 2x + 2y +4z = 10 [6 marks] (d) Find the eigenvalues and eigenvectors of A. [12 marks]

Prove that AB=A(By)=B(Ay) Let A=xD+2 and B=xD-1

When using the cross product it does NOT make a difference if you switch the order of the vectors. In other words A * B = B * A Select one: True False

Identify the function P (x) and Q (x) if the differential equation (1 + cos a) y form + P(2) y = Q (x). sin x (sin x + sin xcosx - y) is written in the de sin z O p(2) = ; Q (x) = sin? a 1+ cos Op(z) sin a 1+ cos ; Q (2) = coS T sin a O p(z) ; Q (2) = sin² x 1 + CoS E O p(2) sin + 1 1+ cos sin a i Q (x) = 1+ cos

Use De Moivre's theorem to change the given complex number to the form a + bi, where a and b are real numbers. {1-sqrt(3)i}^12 A -4096i B) 2048i -2048 D) -2048i E) 12

H.w Find the inverse transform of each of the following. (1) F(s)= s-8 s-3 19 1 (2) F(s)=: s+2 3s-5 6s (3) F(s) = 3 + s2+25 s2+25

Remain Let 3 a= -1 b= -1 -3 a. You start at the origin, move first along the vector a, and afterwards move along the vector b. What are your new co-ordinates? Enter your answer as a vector. (0) a ab sin (a) de f 8 a 92 b. Calculate the angle 0 (in radians) between a and b. Give your answer correct to 3 decimal places 0 8 ab sin (a) Op 1 Submit Assignment

Show that g(x) = 2x² + 3 − 3ª has a real zero using the Intermediate Value Theorem. -

Solve for TA, aA, aB, and aCDon't round off in the solution, just round off the final answer to 3 decimal places, pls show FBD's and complete soln

there is a problem in question a : R=by/b+2y not only b+2y