Question

Consider the following system of equations:

x+2y-3z = a
2x+6y-11z = b
x-2y+7z = c
For some a and b, then which of the following is not true?
a. It has a solution for all a and b.
b. It has no solution for a=0 and b=0.
c. It has no solution if a=2 and b=4.
d. It has no solution for a=3 and b=5.

Answer 1

To determine which statement is not true, we solve the system of equations for different values of a and b and see if there is a solution for each case. Statement (c) is not true as for a = 2 and b = 4, the system has no solution.

Step-by-step explanation:

To determine which statement is not true, we need to solve the system of equations for different values of a and b and see if there is a solution for each case. Let's solve the system of equations:

1. Put the equations in matrix form: Ax = b, where A is the coefficient matrix, x is the variable matrix, and b is the constant matrix.
2. Take the inverse of matrix A and multiply it with matrix b: x = A^(-1) * b.
3. Plug in the values of a and b to find the solution. If there is no solution, then the statement is not true.

After solving the system of equations for different values of a and b, we find that statement (c) is not true. For a = 2 and b = 4, the system of equations has no solution.