linear algebra

i. Find a basis for the column space of A.

ii. Expand your basis for the column space to a basis of the entire range of A.

iii. Find a basis for the null space (or kernel) of A.

iv. Find a basis for the domain of A like that given in Theorem 6.8.

(Theorem 6.8: domain, image, and null spaces)( in applied linear algebra: page252 )

v. Write an explicit formula for all solutions to Ax = b, where b = 4 9 -1 4 ᵀ .

a) es P

2 = P, P is called the

orthogonal projection onto its image space.