Answer to Question #5254 in Linear Algebra for Katelynn Bento
Given Matrix A= |123|
Find the basis of Col A and the dim of Col A
Notice that the matrix A is upper-triangle, so its determinant is a
of diagonal elements:
det(A) = 1*2*3 = 6.
Moreover, det(A) is
Therefore the columns of A are linearly independent and
they constitutive a basis for R^3, so R^3 = Col(A).
any base of R^3 fits to be a base for Col(A),
for instance the columns of
(1,0,0), (2,2,0), (3,3,3)
are the base.
The dimension of Col(A) is the dimension of
R^3 and therefore is equal