Let A be a 3 X 4 matrix. If b = a1 + a2 + a3 + a4
then what can you conclude about the number of solutions of the linear system Ax=b?
Explain.

Let A be a 3 X 4 matrix. If

b = a1 + a2 + a3 + a4

then what can you conclude about the number of solutions of the linear system Ax=b?

Explain.

The system has infinitely many solutions

Step-by-step explanation:

Since b= a1 + a2 + a3+ a4 if it follows that x= (1,1,1,1)^T is a solution to the equation Ax = b.

Since the matrix contains 3 rows there can be 3 nonzero rows and consequently

3 lead variables at most after we compute the row echelon form of the matrix

At least of the variables is free variables is free variable.

The system has infinitely many solutions