For each linear transformation below, state a basis for Ker(T), the Nullity of the transformation, and the Rank of the transformation. If you do not need a vector, then place zeros for all entries of that vector (for example, if you only need 2 vectors for the basis, then fill in the first two vectors and make all subsequent vectors have 0 for all boxes). la +16+lc 1) Let T 2a+3b+3c] -la+(-2)b+ (-2)c 3a+3b+3c i) A basis for Ker(T) would be: ii) The Nullity of T is: iii) The Rank of T is: [la+16+2c+2d 2) Let T(a + bx + cx² + dx³) = la+2b+1c+1d 2a+3b+4c+ 2d -la + (-3)b+ (-1)c+2d] i) A basis for Ker(T) would be: ii) The Nullity of T is: iii) The Rank of T is: T 3) Let T a b de C 3 la+(-1)6+1c+ (-1)d + 2e+4f 2a+(-1)b+4c+4d + 6e + 12f Oa+(-1)b+(-1)c+ (-4)d+ (-1)e + (-2) f 6a+(-3)b+11c + 10d + 18e + 34f i) A basis for Ker(T) would be: 1888 1889 1888 1888-1888)
For each linear transformation below, state a basis for Ker(T), the Nullity of the transformation, and the Rank of the transformation. If you do not need a vector, then place zeros for all entries of that vector (for example, if you only need 2 vectors for the basis, then fill in the first two vectors and make all subsequent vectors have 0 for all boxes). la +16+lc 1) Let T 2a+3b+3c] -la+(-2)b+ (-2)c 3a+3b+3c i) A basis for Ker(T) would be: ii) The Nullity of T is: iii) The Rank of T is: [la+16+2c+2d 2) Let T(a + bx + cx² + dx³) = la+2b+1c+1d 2a+3b+4c+ 2d -la + (-3)b+ (-1)c+2d] i) A basis for Ker(T) would be: ii) The Nullity of T is: iii) The Rank of T is: T 3) Let T a b de C 3 la+(-1)6+1c+ (-1)d + 2e+4f 2a+(-1)b+4c+4d + 6e + 12f Oa+(-1)b+(-1)c+ (-4)d+ (-1)e + (-2) f 6a+(-3)b+11c + 10d + 18e + 34f i) A basis for Ker(T) would be: 1888 1889 1888 1888-1888)
Introductory Circuit Analysis (13th Edition)
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Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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![For each linear transformation below, state a basis for Ker(T), the Nullity of the transformation, and the Rank of the transformation. If you do not
need a vector, then place zeros for all entries of that vector (for example, if you only need 2 vectors for the basis, then fill in the first
two vectors and make all subsequent vectors have 0 for all boxes).
la +16+lc
1) Let T
2a+3b+3c]
-la+(-2)b+ (-2)c 3a+3b+3c
i) A basis for Ker(T) would be:
ii) The Nullity of T is:
iii) The Rank of T is:
[la+16+2c+2d
2) Let T(a + bx + cx² + dx³) =
la+2b+1c+1d
2a+3b+4c+ 2d -la + (-3)b+ (-1)c+2d]
i) A basis for Ker(T) would be:
ii) The Nullity of T is:
iii) The Rank of T is:
T
3) Let T
a b
de
C
3
la+(-1)6+1c+ (-1)d + 2e+4f
2a+(-1)b+4c+4d + 6e + 12f
Oa+(-1)b+(-1)c+ (-4)d+ (-1)e + (-2) f
6a+(-3)b+11c + 10d + 18e + 34f
i) A basis for Ker(T) would be:
1888 1889 1888 1888-1888)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd0e572be-e4a1-4f73-a371-c3cd8962c782%2F3afd3035-66b1-4a69-9665-09c79dfff584%2F57uti7k_processed.jpeg&w=3840&q=75)
Transcribed Image Text:For each linear transformation below, state a basis for Ker(T), the Nullity of the transformation, and the Rank of the transformation. If you do not
need a vector, then place zeros for all entries of that vector (for example, if you only need 2 vectors for the basis, then fill in the first
two vectors and make all subsequent vectors have 0 for all boxes).
la +16+lc
1) Let T
2a+3b+3c]
-la+(-2)b+ (-2)c 3a+3b+3c
i) A basis for Ker(T) would be:
ii) The Nullity of T is:
iii) The Rank of T is:
[la+16+2c+2d
2) Let T(a + bx + cx² + dx³) =
la+2b+1c+1d
2a+3b+4c+ 2d -la + (-3)b+ (-1)c+2d]
i) A basis for Ker(T) would be:
ii) The Nullity of T is:
iii) The Rank of T is:
T
3) Let T
a b
de
C
3
la+(-1)6+1c+ (-1)d + 2e+4f
2a+(-1)b+4c+4d + 6e + 12f
Oa+(-1)b+(-1)c+ (-4)d+ (-1)e + (-2) f
6a+(-3)b+11c + 10d + 18e + 34f
i) A basis for Ker(T) would be:
1888 1889 1888 1888-1888)
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