2) Let T(a+bx+cx² + dx³) = i) A basis for Ker(T) would be: ii) The Nullity of T is: iii) The Rank of T is: la + 2b + 1c + 2d -la + (-1) b+ 0c + (-3) d [ 14+26+1+20-214+ ]
2) Let T(a+bx+cx² + dx³) = i) A basis for Ker(T) would be: ii) The Nullity of T is: iii) The Rank of T is: la + 2b + 1c + 2d -la + (-1) b+ 0c + (-3) d [ 14+26+1+20-214+ ]
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.3: Orthonormal Bases:gram-schmidt Process
Problem 17E: Complete Example 2 by verifying that {1,x,x2,x3} is an orthonormal basis for P3 with the inner...
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Question
![2) Let T(a + bx + cx² + dx³) =
i) A basis for Ker(T) would be:
ii) The Nullity of T is:
iii) The Rank of T is:
·la
3) Let T
b
d e
ii) The Nullity of T is:
=
i) A basis for Ker(T) would be:
iii) The Rank of T is:
la + 2b + 1c + 2d
0a + 2b + 3c+(-1)d
-la+ (-1) b+ 0c +(-3) d
-2a+ (-5) b+ (-4) c+(-3) d
3d]
la + 1b+ (-1) c + Od + le+ (-2) ƒ]
la + 2b + 0c + (-2) d + 2e + (-1) f
Oa + 1b +2c + (-3) d + 3e +2f
2a + 2b + (-3) c + 1d + le+(-5) ƒ]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdef25b02-21c7-4f0b-87c4-78c9bf8df921%2F34f5bf6b-d358-456d-be09-6e34c06a3deb%2F7bnxwh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2) Let T(a + bx + cx² + dx³) =
i) A basis for Ker(T) would be:
ii) The Nullity of T is:
iii) The Rank of T is:
·la
3) Let T
b
d e
ii) The Nullity of T is:
=
i) A basis for Ker(T) would be:
iii) The Rank of T is:
la + 2b + 1c + 2d
0a + 2b + 3c+(-1)d
-la+ (-1) b+ 0c +(-3) d
-2a+ (-5) b+ (-4) c+(-3) d
3d]
la + 1b+ (-1) c + Od + le+ (-2) ƒ]
la + 2b + 0c + (-2) d + 2e + (-1) f
Oa + 1b +2c + (-3) d + 3e +2f
2a + 2b + (-3) c + 1d + le+(-5) ƒ]
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