Suppose the coefficient matrix of a linear system of three equations in three variables has a pivot position. In each column. Explain why the system has a unique solution. Determine h and k such that the solution set of the system (i) is empty, (ii) contains a unique solution, and (iii) contains infinitely many solutions. x_1 +3x_2 =k 4x_1 +hx_2 =8 -2x_1 +hx_2 =1 6x_1 +kx_2 =-2 Consider the problem of determining whether the following system of equations is consistent: 4x_1 -2x_2 +7x_3 = -5 8x_1 -3x_2 +10x_3 = -3 Suppose the coefficient matrix of a linear system of three equations in three variables has a pivot position. In each column. Explain why the system has a unique solution. Determine h and k such that the solution set of the system (i) is empty, (ii) contains a unique solution, and (iii) contains infinitely many solutions. x_1 +3x_2 =k 4x_1 +hx_2 =8 -2x_1 +hx_2 =1 6x_1 +kx_2 =-2 Consider the problem of determining whether the following system of equations is consistent: 4x_1 -2x_2 +7x_3 = -5 8x_1 -3x_2 +10x_3 = -3