TRUE OR FALSE and explain why If the Kernel of a matrix cons

TRUE OR FALSE and explain why.

If the Kernel of a matrix consists only of the zero vector, then the columns of the matrix must be linearly independent. T or F?

Solution

If the kernel of a matrix A consists of the zero vector only, then the column vectors of A must be linearly independent.

because , as the kernel is zero, the columns of A must be linearly independent.

Therefore the solution is True