1. Consider the system of equations Ax = b described by: +2x2 X2 (3k - 4)...

 

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1. Consider the system of equations Ax = b described by: +2x2 X2 (3k - 4) (k − 1)x2 X1 where k is an unknown constant. - X3 +(k+1)x3 = 2 -1 4(k-1) (a) You should not need to do any row operations on an augmented matrix to answer the following questions: i. For what value of k does the system have an infinite number of solutions? For that value of k, describe the solution set in parametric form. ii. For what values of k does the system have no solutions at all? Clearly justify your answers for both values of k that you find. (b) Let k = 0. Find the reduced row echelon form of [A] b] in this case, and hence find the solution vector x. Substitute your solution back into the original system to check its correctness. 1. Consider the system of equations Ax = b described by: +2x2 X2 (3k - 4) (k − 1)x2 X1 where k is an unknown constant. - X3 +(k+1)x3 = 2 -1 4(k-1) (a) You should not need to do any row operations on an augmented matrix to answer the following questions: i. For what value of k does the system have an infinite number of solutions? For that value of k, describe the solution set in parametric form. ii. For what values of k does the system have no solutions at all? Clearly justify your answers for both values of k that you find. (b) Let k = 0. Find the reduced row echelon form of [A] b] in this case, and hence find the solution vector x. Substitute your solution back into the original system to check its correctness.