Question

Hi im struggling with part (b) and (c) of this linear algebra question. Any help would be greatly apprecated

(a) Write down the augmented matrix corresponding to the system of linear equations: + 25 3w W W - + + y y + 1 Na + 4 [2 marks (b) For the remainder of this question the variables v, w, 2, y, and 2 will satisfy a system of linear equations whose augmented matrix is Ab). If the reduced row echelon form of [A6] is: 1 1 4 -2 0 -3 -2 0 0 0 1 5 8 do the following: (i) Parametrize (as a subset of R') the solution space of this system of equations in the variables v, w, x, y, and z. [5 marks] (ii) Determine a basis for the kernel of the matrix A. [3 marks QUESTION 4

Answer 1

...o are linearly independent linearly inde see first and fourth coloumns are and contains pivot element, so o,y are basic variables are free ul F(4W-2X-32) -27 ci and all others 10 . 17 -52 +8 Z -4w] 2x] + Noooob x 3000 + '53xnn 1-47 w 1 + | 27 [ 3 lo+20+ O ooo 01 + OOO cil Basis for Kernel - racow