Question

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

Answer 1

1) IMO 3 -2 7 2 -6 4 8 3 Column space=) Multiply dow I by (-/3) e - 3 22 -73 -6 8 QUESTION WISE ANALYSIS 2 -2 Add 2 times sow I to dow 2 - - 3 213 -7/3 0 0 813 38/3 SOF -2 2 3 Add 3 times 2010 I to sow 3 — пмо 3 %3 -73 o 813 3613 0 -4 Multiply yow 2 by (3/6) ) 3 - 7/3 QUESTION WISE ANALYSIS 19/4 VO - 0 O -4 g Add to y times sow 3 to sow 2 -3 23 23 o i canned with CS CamScanner PP o

Add ½ times do W 3 to row I ÖWT -3 213 O LO o 0 Add 2 times dow 2 to you 1 TOPIC WISE ANALYSIS 3 O อ 0 O co 0 0 SOF Recall that a leading one is the first nonzero entry in a row, the Columns Containing deading Ohes are the pivot columns. To obtain a basis for the column space, we just use the pivot columns from the original Matrix. 73 CS Scanned (with owie {F}.0). {{]} 7 8 4 م CamScanner

SOF for dow spac8 > 3 9 - 2 7 2. -6 4 8 3 -9 multiply now I by 1/3) and Add 2 times rool to row 2 2 QUESTION WISE ANALYSIS -3 23 -73 88/3 O 3 -2 2 2/3 Add 3 times sow I to sow 3 3 - / 3873 -4 9 IMO 0 813 multiply row 2 by 3/8 and Add u times row a to SOF how 3: 3 2/3 -7/3 O 194 O O 28 mutltiply dow 3 by ) QUESTION WISE ANALYSIS and Add (194) timea 200 3 to row 2 43 3 - 0 O IMO CS Scanned with I QUADZAMERA

DORINGSOM Add 7 times sow 3 to dow and Add -% timea row 2 to dowl - 3 0 O con o 0 ل the nonzero dowe in the reduced dow echelon form are basis for the dow space 0, [l o] co, [o, 0, 1] ICS Cambcanner -3) 09 O, CHRICE O'YMPIAD FOUNDATION Scanned With