linear equations

Consider the system of linear equations x + 2y + z = 5 2x + ay + 4z = 12 2x + 4y + 6z = b The values of a and b such that there exists a non-trivial null space and the system admit...

The set of equations x + y + z = 1 ax - ay + 3z = 5 5x - 3y + az = 6 has infinite solutions, if a =

A person divided an amount of Rs. 100,000 into two parts and invested in two different schemes. In one he got 10% profit and in the other he got 12%. If the profit percentages are...

Gauss-Seidel method is used to solve the following equations (as per the given order). $$${x_1} + 2{x_2} + 3{x_3} = 5$$$ $$$2{x_1} + 3{x_2} + {x_3} = 1$$$ $$$\,3{x_1} + 2{x_2} + {x...

Solve the system $$2x+3y+z=9,$$ $$4x+y=7,$$ $$x-3y-7z=6$$