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Linear Algebra With Applications
Found in: Page 289
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

Find the determinants of the linear transformations in Exercises 17 through 28.

18. T(f)=2f+3f' from P2 to P2

Therefore, the determinant of the linear transformations is given by,

det T =det B=8.

See the step by step solution

Step by Step Solution

Step 1: Definition. 

A determinant is a unique number associated with a square matrix.

A determinant is a scalar value that is a function of the entries of a square matrix.

It is the signed factor by which areas are scaled by this matrix. If the sign is negative the matrix reverses orientation.

Step 2: Given. 

Given linear transformation,

Tf=2f+3f' from P2 to P2

Step 3: To find determinant.

Forwe fP2 have ft=at2+bt+c. So we compute

Tft =2ft+3f'tTft =2at2+bt+c+32at+bTft =2at2+(6a+2b)t+(3b+2c)

Since B=t2 ,t,1 is a basis for P2, the matrix of T corresponding to B is



det T =det B = 8.

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