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-intercept
x-intercepts or the zeros of the functions or roots
graph of the function, given vertex is at (-2, -9)
Solve the system of linear equations (4 marks)
2x + 5y = 3
– x + 6y = 8
Resolve into Partial Fraction (4 marks)
Simplify: (4 marks)
Given find the inverse function. (4 marks)
Write the names of curves, given their equations: (5 marks)
x2/16 + y2/9 = 1
3y = 2x + 5
(x - 5)2 + (y + 6)2 = 25
x2/16 – y2/25 = 1
y = 2x2 + 10x + 25
Solve, write your answer in interval notation : (4 marks)
Using synthetic division divide by (4 marks)
Write down the first five terms of the arithmetic progression with the first term 8 and common difference 7, then find the 17th. (4 marks)
Write down the first five terms of the geometric progression with the first term 3 and common ratio 2, then find the 17th. (4marks)
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#4 Complete the squares. a) x2 + 4x - y - 12 = 0 for x b) 2x + y2 - 6y = 1 for y #5 Solve the system of equations sx - y = 11 a) 12x + y = 19 1-3x - 2y = 1 b) 16x + 4y = -2
q2 please find x1.x2.x3.x4 using matlab &73 3:45 zain JO 4ll ring Q1 a function with the name "Area Circumference" to calculate the area and circumference tput) of a rectangle. Define the inputs of this function as required. (6marks) rite a manuscript to solve the following system of equations based on [A][x] =[b)]. Find x1, x2, . (5 Marks) 2x1+ x2-3 +2x4 4 x1+5x2-3ax3 +604 -2x1 +5a2-2r3 +6x4= 4 4x1+11x2-4x3+8x4 = 5 Q3: Having f(x) = 3x6-13x2 + 2x, Integratef...
1. Find parametric equations for the line passing through the center of the spheres. Hint: Complete the square three times to rewrite the equations of the spheres so they are in the form (x - h)2 + (y - k)2 + (x - 1)2 = r. 32 + y2 + z2 - 2x - 4y + 4z = 8 x2 + y2 + x2 + 2x + 6y + 4z = 20
Question 4 -1 (a) 114- find C so that 4 =BCB- [8 marks) (6) ITA = }; and B = (-2 21. find matrices X such that 2A + x = 8 (5 marks) c) Three simultaneous equations are given as below: * + y y + 256 - y - 3 c 0 (11) Write the simultaneous equations above & matrix equation [4 marks] Solve the simultancous equations above by using inverse matrix method [5 marks] Give the expression...
q3 please using matlab zain Jo. Ø 73 3:45 • nering Q1: a function with the name "Area Circumference to calculate the area and circumference tput) of a rectangle. Define the inputs of this function as required. (6marks) Write a manuscript to solve the following system of equations based on (A]x] =[b]. Find x1, x2 4. (5 Marks) 2x1 + x2-03 + 2x4 = 5 4x1 +5x2-3x3 + 6x4 = 9 -2x1 +5x2 - 2.03 + 6x4 = 4 4x1...
DIFFERENTIAL EQUATIONS / Linear Algebra Only people that are proficient in DIFFERENTIAL EQUATIONS should even attempt to solve. No beginners or amateurs allowed. Please write clearly and legibly. No sloppy Handwriting. I must be able to clearly and easily read your solution and answer. Circle final answer. 8.3.14 Question Help Find the first four nonzero terms in a power series expansion about x = 0 for a general solution to the given differential equation. (x2 + 2)y"+y=0 y(x) = 0...
1. (a) Express the following system of equations in augmented matrix form. 2x - 4y + 5z = 9 x + 3y + 8z = 41 6x + y - 3z = 25 (2 marks) (6) Use Gaussian elimination to solve the system of equations. (6 marks) 2. Given that a matrix A: 18 A= 1 8 -1 4 -1 -1 -1 8 (a) Determine AT. (6) Calculate the det (A). (2 marks) (6 marks) 3. Refer to the graph...
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....
19. Find the critical points, relative extrema, and saddle points of the function. a. f(x, y) = x2 + y2 +2x – 6y + 6 b. f(x, y) + y2 c. f(x, y) = x2 – 3xy - y2 = x²
Question 5 (Unit 6) - 31 marks (a) Express the following inhomogeneous system of first-order differential equations for x(t) and y(t) in matrix form: = 2x + y + 3e", y = 4x – y. Write down, also in matrix form, the corresponding homogeneous system of equations. (b) Find the eigenvalues of the matrix of coefficients and an eigenvector corresponding to each eigenvalue. (c) Hence write down the complementary function for the system of equations. (d) Find a particular integral...