Find the kernel of the linear transformation. (if

Ответ:

martina28

14.03.2022

Kernel is the set of all elements of the form

a_1x+a_2x^2+a_3x^3+a_4x^4+a_5x^5

Step-by-step explanation:

We are given that a linear transformation

T: $P_5\rightarrow R$

T(a_0+a_1x+a_2x^2+a_3x^3+a_4x^4+a_5x^5)=a_0

We have to find the kernel of the linear transformation if all real numbers are solutions

Kernel: It is defined as set of elements whose image is zero.

i.e T(x)=0 for any x belongs to domain.

To find the kernel of given linear transformation we substituting the given function is equal to zero

T(a_0+a_1x+a_2x^2+a_3x^3+a_4x^4+a_5x^5)=0

a_0=0

Therefore, the basis of kernel of given linear transformation is

K= $\left\{x,x^2,x^3,x^4,x^5\right\}$

Kernel is the set of all elements of the form

a_1x+a_2x^2+a_3x^3+a_4x^4+a_5x^5

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