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Question 3. (20 pts) Let A= -3 9-27 2 -6 4 8 3 -9 -2 2 Find a basis for Col(A) and a basis for Nul(A).


Question 4. (15 pts) Let the matrix A be the same as in Question 3. (1). Find the rank of A. (2). Find the dimensions of Nul(
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③ The given matrice is A= -3 % 2 - 6 -2 1 + 8 2 - -2 2 we appely elemen fany To O operation 0 1 . RI 2. R2 PR 6 g 4 & - 2 1 2chalaga O 4 19 0-28 O C3=43 R2 = 28 R2 0 119 0 o 0 e4 = 4 44-194 $ 0 EB, 0 0 B is a matrix. no w echelon det X=(x, yz, w) € NTherefore Nuu(A) = 1 se($):CER Since Row echelon matrine B Contains beading 1 in 1st, 3rd 4th colunan then and 7 colcas a spa41) rank (A) = number of element in basis for Col(A) 3 dim (Nul(A)) a number of element in basis for NUICA) I. dim (.col (A))

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