You & maths

Exercise Set 1.1 – No. 11

11. In each part, solve the linear system, if possible, and use the result to determine whether the lines represented by the equations in the system have zero, one, or infinitely many points of intersection. If there is a single point of intersection, give its coordinates, and if there are infinitely many, find parametric equations … Read more Exercise Set 1.1 – No. 11

Exercise Set 1.1 – No. 10

10. In each part, determine whether the given 3-tuple is a solution of the linear system: Consider the linear system  and 3-type . Observe  that which gives us that the 3-type does not satisfy the equation x+2y-2z=3 and therefore is not a solution of the linear system above. Consider the linear system  and 3-type . … Read more Exercise Set 1.1 – No. 10

Exercise Set 1.1 – No. 9

9. In each part, determine whether the given 3-tuple is a solution of the linear system ‘For each part put the values of x1, x2 and x3 atest whether the values equals the all ones vector in RHS or not.  The matrix   The vetor in part (a) is x=(3, 1, 1). Ax = (1, … Read more Exercise Set 1.1 – No. 9

Exercise Set 1.1 – No. 6

6. Fnd a linear system in the unknowns x1,x2,x3,…, that corresponds to the given augmented matrix. Consider the matrix We have that the linear system of two equations in the four unknowns x1, x2, x3, and x4 given by  has A as its augmented matrix. Consider the matrix We have that the linear system of … Read more Exercise Set 1.1 – No. 6

Exercise Set 1.1 – No. 5

5. Fnd a linear system in the unknowns x1,x2,x3,…, that corresponds to the given augmented matrix. Since these are augmented matrices, the final column of an m x n matrixis always the solution to . The coefficientsof are all of the numbers to the left of the final column, with each rowrepresenting a single linear … Read more Exercise Set 1.1 – No. 5

Exercise Set 1.1 – No. 4

4. Write down the augmented matrix for each of the linear systems in Exercise Set 1.1 – Number 3. a) The augmented matrix of the system: where x1, x2 of problem 3a is b) The augmented matrix of the system: of problem 3b is c) The augmented matrix of the system: of problem 3c is

Exercise Set 1.1 – No. 3

3. Using the notation of Formula: Write down a general linear system of a) two equations in two unknowns. b) three equations in three unknowns. c) two equations in four unknowns. a) A general linear system of two equations in two unknowns can be written as: where x1 and x2 are the unknowns. b) A … Read more Exercise Set 1.1 – No. 3

Exercise Set 1.1 – No. 2

2. In each part, determine whether the equation is linear in x and y. The equation  is linear in x and y. The equation  is not linear x and y due to the terms and . The equation  is linear in and x and y. The equation  is not linear in x and y due … Read more Exercise Set 1.1 – No. 2