Question

2 3 -6 9 0 1 -2 0 3. Let A= 2 -4 7 2 The RREF of A iso 0 1 3 -6 6 -6 0 0 0 (a) (6 points) Find a basis for Col A, the column space of A. 0 (b) (2 points) What is rank A? (c) (6 points) Find a basis for Null A, the null space of A. (d) (2 points) What is the dimension of the null space of A?

Answer 1

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a we can norice that the ibr and 3rod columns of pivot columns. to them them will RREF (*) arse so, columns of a commenponding form for col(a). a basis . (م) ام so, basis for col (A) is {[3] [ 6 2 since basis for col(A) contains a recross, so rank (A) for we have, BREF (A) .x=0 implies Now x= [X,1 mg, X.,ka] non-null vecton a M, -239 - 634 =0 ^3 + 204 =0 600 => x= 2x2 + x2 = 122 + 0 *3 = 0x2 - 23 94 = 0 X2 +124

so, basis for null space is, {[i] [] 6 Since Null (n) basis contains two vectors, so dimension of Null (A) 2