Can someone explain why Ax is in col(A) if (A^T)Ax=0, A^T is the transpose.
Note: Ax is also orthogonal to col(A),(so x=0) so don't let that confuse you.
y''-2y'+y=6/(x^3)*e^x
the sollution to the homogenous equation is e^x and x*e^x, so how do I solve for the particual sollutioin, how do I choose the undetermined coefficients? I have tried:
(c + c1/x+c2/x^2+c3/x^4)*e^x and (cx^2+c1x+c2+c3/x), but none of them seems to give a good answer...
To find the column space of a matrix, you reduce the matrix and those columns that contains leading variables(pivot columns), refers to the columns in the original matrix who span the columnspace of the matrix. But does the pivotcolumns in the reduced matrix also span the column space of the...