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Linear Algebra With Applications
Found in: Page 402
Linear Algebra With Applications

Linear Algebra With Applications

Book edition 5th
Author(s) Otto Bretscher
Pages 442 pages
ISBN 9780321796974

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Short Answer

Consider the transformation T(q(x1,x2))=q(x1,0) from Q2 to P2. Is T a linear transformation? If so, find the image, rank, kernel, and nullity of T.

the solution is

Yes,T is a linear transformation.

ker(T)=qx1,x2=bx1x2+cx22Q2:b,cRIm(T)=p(x)=ax2P2:aRrank(T)=1and nullity (T)=2

See the step by step solution

Step by Step Solution

Step 1: given information


Step 2: linear transformation

Consider q1x1,x2=a1x12+b1x1x2+c1x22

q2(x1,x2)=a2x12+b2x1x2+c2x22Q2 and αR then9


Since T satisfy

T(αq1+q2)=αT(q1)+T(q2)forαR and q1,q2Q2

T:Q2P2,T(q(x1,x2))=q(x1,0)is a linear transformation.

Step 3: find kernel of T and image of T

Kernel of T:


Image of T:



Step 4: conclusion

Yes, is a linear transformation.

ker(T)=q(x1,x2)=bx1x2+cx22Q2:b,cRIm(T)=p(x)=ax2P2:aRrank(T)=1 and nullity (T)=2

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