Let A = and wetine if w is in Col(A). Is w in Nul(A)? -4 12 Determine if w is in

ID: 3282043 • Letter: L

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Let A = and wetine if w is in Col(A). Is w in Nul(A)? -4 12 Determine if w is in Col(A). Select the correct choice below and, if necessary, fill in the answer box to complete your choice O A. The vector wis in Col(A) because the columns of A span R2 The vector w is in Col(A) because Ax = w is a consistent system. One solution is x ° C. The vector w is not in Col(A) because Ax-w is an inconsistent system. One row of the reduced row echelon form of the augmented matrix [A 0] has the form [0 0 b] where b- D. The vector w is not in Col(A) because wis a linear combination of the columns of A. Is w in Nul(A)? Select the correct choice below and fill in the answer box to complete your choice. (Simplify your answer.) .x A. The vector w is not in Nul(A) because Aw . Bl 10 B. The vector w is in Nul(A) because Aw:

Explanation / Answer

Let C1 denote first column of A and C2 the second column

So, C2=-3C1

Aw=3C1+C2=3C1-3C1=0

Hence, w is in Nul(A)

Also we see that

C1=-4w,C2=12w

Hence, w is in Col(A)

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Let A = and wetine if w is in Col(A). Is w in Nul(A)? -4 12 Determine if w is in

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