Question 4 -1 (a) 114- find C so that 4 =BCB- [8 marks) (6) ITA =...
3. (10 points) Simultaneous left inverse The two matrices 3 2] and both left-invertible, and have multiple left inverses. Do they have a common left inverse? Explain how to find a 2 × 4 matrix C that satisfies CA-CB-1, or determine that no such matrix exists. (You can use numerical computing to find C.) Hint. Set up a set of linear equations for the entries of C. Remark. There is nothing special about the particular entries of the two matrices...
32. Simplify : a. x/3-x/4 b. 3/(2x) -4/x c. 1/2x-1/3x 33. Find x if: 3x +6 = 2-5x a. b. x/m + x/n = 1 C 1/x = 3/m d. Sx/3 = 2 34. Find b if: x/(x+a) = 2/b a. b. v(x - b') =y 35. Solve the following Simultaneous linear equations and check in both equations: a) 3x+y=-4 x-2y 1 b) 5x+y=-8 2x-2y 4 Answer: x-1, y.3 36. Evaluate the expression below, if b-3 and c-2. 2bc'+(bc) Helpful...
Question 4: [25 Marks] Solve the Questions 4a to 4c using the Matrix Algebra (By the Inverse method or Cramer's Rule) (a) Supply and demand models analysis can also involve more than two markets. Find Given the demand finction P+20+6040 And the supply funcon the equilibrium prices (P, P2,Pa) and quantities (Q, O, Qa) for the three substitute goods below [10 Marks] Use the substuion method sove P in terms of Q and use the quadraic fom (b) Given a...
1. Find a 2x2 matrix A if for the vector v= [R], Av = [4 +38] 2. For this problem, use matrices A = La ), B=1 _Jandc=lo 9]. Suppose that the matrices A and B commute (so AB=BA) and the matrices A and C commute. Find the entries for the matrix A. 3. Find a number a so that the vectors v = [3 2 a) and w = [2a -1 3] are orthogonal (perpendicular). 4. For the vector...
F GHANA served) TEF RO HC 3 -2 0 A2. Given the matrix below 5 marks) [5 marks (10 marks (b) Compute explicitly the eigenvalues and determine the determinant, (c) Compute the corresponding eigenvectors of the matrix above (a) Show that the matrix is positive definite. 1 | so that the characteristic polynomial 5 marks 0 (d) Choose a, band c in the matrix B = | 0 Based on Cayley-Hamilton's theorem, every matrix fulfills its characteristic polynomial, using the...
4. Solve the following system of linear equations using the inverse matrix method. 1 y = 1 2 , 3 2 -r- 1 5 4 a) x+y +z= 6 x-y-3z=-8 x+y- 2z=-6 b) Solve the following system of linear equations using Cramer's Rule. 5. 2 1 -X- 3 2 1 3 X+-y-1 5 4 y = 1 a) x+y+z= 6 x-y-3z=-8 x+y- 2z = -6 b)
4. Solve the following system of linear equations using the inverse matrix method. 1...
Question 2 (25 Marks) 73-6 a Express 7- in partial fraction form and then Find the inverse Laplace transform of using the partial fraction obtained. b. Find the inverse Laplace tansforms of 2 c. Solve y(t) +y(t) cos 2t. y(o) 8 Marks] [8 Marks] 9 Marks] 23+5 0.y (o) 1 by using Laplace transform method.
Directions: Write your complete solution in EACH QUESTION Give an example of a matrix with dimension 3X2. Also find its transpose. (3 marks) What is the value of x : (4 marks) 3(x + 3) = Given: y = x2 + 4x – 5 Find the following (6 marks)y-interceptx-intercepts or the zeros of the functions or rootsgraph of the function, given vertex is at (-2, -9) Solve the system of linear equations (4 marks)2x + 5y = 3 – x + 6y = 8 Resolve...
XTAX=1. determine their canon- 1. Write the following quadratic forms as V(x) ical forms, find the modal matrices (i.e. the matrices of unit eigenvectors) of the corresponding transformations and write down explicite expressions for canonical cOordinates (y1, 2, y3) in terms of the original coordinates (x1, X2, X3). State what surfaces these quadratic forms correspond to = > (a) x + 4x1r2 + 4a13-8a2x3 = 1; (b) a3a3a^ + 4xj2 +4x131223 1; (c) 4a7 2a2 2axjx2 2x13+ 6x23 = 1....
QUESTION 1 (15 MARKS) a) Given 4'{+93}=LC }-( - siu (au) sin’au) sin(2t - 2u) du. Use the convolution theorem to determine the value of constant a. (5 marks) b) Using Laplace transform, solve the simultaneous differential equations dac dt - 4 =1+t, +2=t-1. dt given that x(0) = 0 and y(0) = 3. (10 marks)