Question

Find a basis for Col(A) and a basis for Nul(A) in the context of a matrix A.

A) Col(A): {(1, 0), Nul(A): {(0, 1)}
B) Col(A): {(1, 0, 0), Nul(A): {(0, 1, 0)}
C) Col(A): {(1, 1), Nul(A): {(1, -1)}
D) Col(A): {(1, 1, 1), Nul(A): {(1, -1, 1)}

Answer 1

To find a basis for Col(A), we need to find the column vectors that form the span of the matrix A. The basis for Col(A) is the set of linearly independent columns of A. To find a basis for Nul(A), we need to find the vectors that satisfy the equation A*x=0. The basis for Nul(A) is the set of linearly independent solutions to the equation.

Step-by-step explanation:

To find a basis for Col(A), we need to find the column vectors that form the span of the matrix A. The basis for Col(A) is the set of linearly independent columns of A. To find a basis for Nul(A), we need to find the vectors that satisfy the equation A*x=0. The basis for Nul(A) is the set of linearly independent solutions to the equation.

Looking at the options given, option C is the correct answer. The basis for Col(A) in option C is {(1, 1)}, and the basis for Nul(A) is {(1, -1)}.