2.4 (10 points) For which value(s) of a does the system 21+ 2+ x3 = 1 21+ 2x2+ ax3 = 2 2:01+ ax2+ 4x3 = a? have (i) a unique solution, (ii) no solution, (iii) infinitely many solutions? Where the system has infinitely many solutions, write the solutions in parametric form.

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mdasfaaruddinshareefLv10

15 Jun 2023

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6. Consider the following system of equations, depending on the parameter k. 21 +(k+1):22 +4x3 = 3 +(k+ 3x3 = 21 +222 +3x3 = . Which of the following is true? A) The system has a unique solution for every value of k. B) The system has no solution for any value of k. (C) The solution is unique if k = -1 and k + 2. There are no solutions if k = 2 or if k = -1. D) The solution is unique if k #1 and k #2. There are no solutions if k = 2 and infinitely many if k=-1. E) None of the above.

1. (10pts) (a) Find the values of k for which the system -k x + y + k” = 0 = 4 x+2y + (kP+4)2 = k has (i) a unique solution (ii) no solution (iii) infinitely many solutions.

].x = 23 ), and b = [ ]. Then the 1 2-21 6. Let A = 1 system of linear equations Ax=b (a) has a unique solution if and only a -1. (b) has no solutions if and only if a=3. (c) has infinitely many solutions if and only if a = 1 (d) has a unique solution for every value of a. (e) None of the above

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2.4 (10 points) For which value(s) of a does the system 21+ 2+ x3 = 1 21+ 2x2+ ax3 = 2 2:01+ ax2+ 4x3 = a? have (i) a unique solution, (ii) no solution, (iii) infinitely many solutions? Where the system has infinitely many solutions, write the solutions in parametric form.

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