2. (a) Consider the following linear system of equations where k € R. x+y+z=7 x+y=z=5 -x=y+z= k (i) What value of k will

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2 A Consider The Following Linear System Of Equations Where K R X Y Z 7 X Y Z 5 X Y Z K I What Value Of K Will 1 (50.58 KiB) Viewed 40 times

2. (a) Consider the following linear system of equations where k € R. x+y+z=7 x+y=z=5 -x=y+z= k (i) What value of k will give an infinite number of solutions? Justify your choice. [2 marks] (ii) Using your value for k, form an augmented matrix, and reduce it to reduced row echelon form. [3 marks] (iii) Using information from your matrix in (ii), produce the vector equation along which all solutions will lie. of the line [3 marks] (b) For which 3 values of k will elimination using row operations fail to give 3 pivots (or leading variables)? Justify each choice based on the row and column structure of your matrix. You do not need to row reduce the matrix. [3 marks] [k 3 4 A = k k 2 kkk