Question

For each of the following augmented matrices, decide whether or not the corresponding system has no solution, a unique solution, infinitely many solutions with one parameter or infinitely many solutions with two parameters. -1-2 -1-2 1 -3 4 - H -1-4 -4-2 1 -3 -4 4 1-5 0 -3 -3 -2 0 -4 3 -3 3 0 2 -1 7 2 1 A = B = 0 C = 0 0 0 -2 -3 2 -9 and 0 0 3 3 1 0 0 0 0 0 0-7 0 0 0 0 0 0 0 0 0 0 0 0 Select all correct statements below. (This question is graded as the number of correct selections minus number of incorrect selections.) The augmented matrix A represents a system of equations with no solution. The augmented matrix A represents a system of equations with a unique solution. The augmented matrix A represents a system of equations with infinitely many solutions with one parameter. The augmented matrix A represents a system of equations with infinitely many solutions with two parameters. The augmented matrix B represents a system of equations with no solution. The augmented matrix B represents a system of equations with a unique solution The augmented matrix B represents a system of equations with infinitely many solutions with one parameter. The augmented matrix B represents a system of equations with infinitely many solutions with two parameters. The augmented matrix C represents a system of equations with no solution. The augmented matrix C represents a system of equations with a unique solution. The augmented matrix C represents a system of equations with infinitely many solutions with one parameter The augmented matrix C represents a system of equations with infinitely many solutions with two parameters.

Can you please explain how did you arrive to that answer. thanks

Answer 1

sony for matrix A the correct option is > The augmented matrix A represents a system of equations with infinitely many solutions with two parameters, for matrix B the correct option is . we have 345 = 4 > 15=4 214-25 = 7 > 204 = 7+4 = 23 ) ny= 25 - -2 -343-320-15 =-2 = -343 > -343 = -2+4 +25 = -12 18 * → -343 = -> 3 = -74 2,-342 +424-25=-2 > y=-2 +372 +4(25) + 4 Here we have Hz as - one parameter.

So for augmented matrix B we have •The augmented matrix B represents a system of equations with infinitely many solution with one parameter. for augmenteel matrix C = [T/b] Here we have Rank (T) = 3 # Rank (c) = 4 Hence the system has not solution. Therefore correct option is » The augmented matrik o represents system of equation coith no solutions . Abore is our required solution.