Suppose T: P3→R³ is a linear transformation whose action is defined by a-2b+5c-4d T(ax³ + bx²+cx+d) = 3a-b+5c-2d a-b+3c-2d Determine whether T is one-to-one and/or onto. If it is not one-to-one, show this by providing two polynomials that have the sam the image of T. Use the '^' character to indicate an exponent and x as the variable for polynomials, e.g. 5x^2-2x+1 T is one-to-one T is onto

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Suppose T: P3→R³ is a linear transformation whose action is defined by
a-2b+5c-4d
T(ax³ + bx²+cx+d) = 3a-b+5c-2d
a-b+3c-2d
Determine whether T is one-to-one and/or onto. If it is not one-to-one, show this by providing two polynomials that have the sam
the image of T. Use the '^' character to indicate an exponent and x as the variable for polynomials, e.g. 5x^2-2x+1
T is one-to-one
T is onto
Transcribed Image Text:Suppose T: P3→R³ is a linear transformation whose action is defined by a-2b+5c-4d T(ax³ + bx²+cx+d) = 3a-b+5c-2d a-b+3c-2d Determine whether T is one-to-one and/or onto. If it is not one-to-one, show this by providing two polynomials that have the sam the image of T. Use the '^' character to indicate an exponent and x as the variable for polynomials, e.g. 5x^2-2x+1 T is one-to-one T is onto
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