&Suppose that a linear system has its augmented matrix as follows: [3 2 1 1 0 1 3 2 0 1ca] For which value(s) of a and e will the system have (i) no solution (ii) a unique solution and (iii) multiple solutions.

Assume that the following augmented matrix represents a system of linear equations. -1 -8 2 -1 -2 -20 -8 -1 -1 -14-3 What kind of solution does this system have? (A) infinitely many solutions with 2 arbitrary (free) parameters (B) 3 solutions (C) infinitely many solutions with 1 arbitrary (free) parameter (D) 2 solutions (E) unique solution (F) infinitely many solutions with 4 arbitrary (free) parameters (G) infinitely many solutions with 3 arbitrary (free) parameters (H) no solution A O B O E G H

6). Determine the solution for the following augmented matrix for a 3x3 linear system of equations. y r3 6. (x, y, z) = ( ) -9 18 Lo 7 | 14. O ON

Let A be a 3x3 matrix, and let u₁ and u₂ be the first two columns of A. Assume that u₁ and u₂ are not parallel. If a linear system Av = b has infinitely many solutions, what can we say about the third column u3 of A, in terms of u₁ and u₂? In other words, how does u3 relate to u₁ and u₂?