Question

If the columns of matrix A are linearly dependent, then there exists a nonzero solution to the equation Ax = 0.

a. True
b. False

Answer 1

If the columns of matrix A are linearly dependent, then there exists a nonzero solution to the equation Ax = 0. True.

Step-by-step explanation:

True. If the columns of matrix A are linearly dependent, it means that one column can be written as a linear combination of the other columns. This implies that the system of equations represented by Ax = 0 has infinitely many solutions, including a non-zero solution.

For example, if A = [1 2; 3 6], the second column is a scalar multiple of the first column. Therefore, the equation Ax = 0 has a non-zero solution.