Question

does the matrix equation ax = b always have a solution for every choice of the vector b in r 3 ? justify your answer.

Answer 1

Yes, the matrix equation ax = b always has a solution for every choice of the vector b in r3.

Step-by-step explanation:

Yes, the matrix equation ax = b always has a solution for every choice of the vector b in r3.

To justify this, we need to understand that if a matrix has a non-zero determinant, then it is invertible. In other words, if the determinant of the coefficient matrix A is non-zero, then the matrix equation has a unique solution. Since we are given a vector b in r3, we can conclude that the matrix equation ax = b will have a solution for every choice of b in r3.

Therefore, the matrix equation ax = b will always have a solution for every choice of the vector b in r3.