# Answer to Question #1341 in Linear Algebra for AA

Question #1341

Let A = (-2 -1 -3 6 1 // 1 1 1 -2 1 // 2 3 1 -2 4 ) Find a basis for the column space Col(A) of A, and a basis for the null spaceNul(A) of A.Show that for any matrix A, if u and v are in the null space of A, then

so is u + v.

so is u + v.

Expert's answer

Col(A) = (-2 -1 1 | 1 1 1 | 2 3 4)

because det(Col(A)) not = 0

Nul(A) = ker(A)= (2 -1 1 1 0)^T

because A*( Nul(A)*k ) = 0, where k is any real number

because det(Col(A)) not = 0

Nul(A) = ker(A)= (2 -1 1 1 0)^T

because A*( Nul(A)*k ) = 0, where k is any real number

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