All the parts I got wrong could you help me out with/try to explain how you got

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All the parts I got wrong could you help me out with/try to explain how you got there, I had trouble understanding what the question was asking

Midterm Page 5 of 6 February 3, 2017 Math 308 I n x m a. For which n is iii E Rn b. For which n is the column space of A a subspace of R"? since there exis a mutt spa of (u uz) the correspond in in RE F form a bari c. What is the dimension of the column space of A? dim col (A)) rank (A) 3 rank t null ty 5 (2) d. How many linearly independent rows does A have? of ru ws with leading l'c rank (A ei. If Bo is a vector such that Aro bo. Write down the general solution to the equation

Explanation / Answer

a) n = 5 ,since u1 is basis for null space

null space is {x : Ax = 0}

A is of dimension (4*5) , so x has to be (5* _ ) for Ax to be valid ,hence

n= 5

b) n = 4, In linear algebra, the column space (or range) of a matrix A is the span (set of all possible linear combinations) of its column vectors.

column vectors have size equal to number of rows.

hence n = 4

c) dim (column space ) = 3

rank+nullity is the number of all columns in the matrix A.

nullity = 2

hence rank = 5-2 = 3

d)rank = 3

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