If the system of linear equationsx−2y+z=−42x+αy+3z=53x−y+βz=3has infinitely many solutions, then 12α+13β is equal to

Consider the following system of linear equations,x + 2y − 3z = a2x + 6y − 11z = bx − 2y + 7z = cwhere a, b and c are real constants. Find the condition for a, b and c such that this system of linear equationshas at least one solution

Consider the following system of linear equations:x-y+2z=1,2x+y+3z=3,x+3y+z=2.What is the solution to this system?

Consider the following system of equations.x + y − z = 12x + 3y + kz = 3x + ky + 3z = 2Using the Gaussian elimination method, find the values of k for which the system has,(a) no solutions(b) unique solution(c) infinitely many solutions(d) Find the solutions of the system for the cases (b) and (c)

Consider the linear systemx + y + z = 1x + (a + 2)y + 2z = 5x + 7y + (a + 1)z = 9.Determine the values of a such that the system has(a) no solution(b) a unique solution(c) infinitely many solutions

Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.2, x, plus, 3, y, equals, minus, 12x+3y=−14, x, plus, 6, y, equals, 14x+6y=1