Assignment:
Q1. Which of the following sets of vectors are bases and why are they bases for P2
A) 1-3x+2x^2, 1+x+4x^2, 1-7x
B) 4+6x+x^2, -1+4x+2x^2, 5+2x-x^2
C) 1+x+x^2, x+x^2, x^2
Q2. In each part use the information in the table to find the dimension of the row space, column space and null space of A and the null space of AT
Note A = a thru g
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a
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b
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c
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d
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e
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f
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g
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Size of A
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3 x 3
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3 x 3
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3 x 3
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5 x 9
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9 x 5
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4 x 4
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6 x 2
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Rank (A)
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3
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2
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1
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2
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2
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0
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2
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Q3. Find a basis for the null space of A.
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1
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-1
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3
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a)
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A=
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5
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-4
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-4
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7
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-6
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2
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2
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0
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-1
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b)
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A=
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4
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0
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-2
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0
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0
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0
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1
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4
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5
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2
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c)
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A=
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2
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1
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3
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0
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0.1
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3
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2
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2
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1
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4
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5
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6
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9
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3
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-2
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1
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4
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-1
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d)
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A=
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-1
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0
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-1
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-2
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-1
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2
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3
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5
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7
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8
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1
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-3
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2
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2
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1
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0
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3
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6
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0
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-3
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e)
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A=
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2
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-3
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-2
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4
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4
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3
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-6
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0
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6
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5
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-2
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9
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2
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-4
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-5
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Provide complete and step by step solution for the question and show calculations and use formulas.