These kinds of explanations are so meh to me. Linear algebra is useful once you begin to look for vector spaces you didn't know you had.
Thinking of matrices as spreadsheets is barely abstraction. Seeing the derivative operator represented as a matrix, acting over the polynomial vector space can open your eyes.
Taking the determinant of that matrix shows that d/dx isn't invertible.
Thinking of the fixed point of the transformation yields exp, the eigenfunction of the operator.
Thinking of matrices as spreadsheets is barely abstraction. Seeing the derivative operator represented as a matrix, acting over the polynomial vector space can open your eyes.
Taking the determinant of that matrix shows that d/dx isn't invertible.
Thinking of the fixed point of the transformation yields exp, the eigenfunction of the operator.