If $A$ is a square matrix with linearly dependent columns, then $A$ is not invertible.
Why is this true for matrices?
[Math] Why is this true for matrices? Linearly dependent columns $\implies$ not invertible
linear algebramatrices
linear algebramatrices
If $A$ is a square matrix with linearly dependent columns, then $A$ is not invertible.
Why is this true for matrices?
Best Answer
You should know that elementary column operations preserve a zero/nonzero determinant. You should also know that if a column is all zeros, then the determinant is zero. All that remains is to convince yourself that if the columns are linearly dependent, then you can make one column all zeros from a sequence of elementary column operators.