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Chapter 4: Q44E (page 200)

Question: TRUE OR FALSE?

4. The kernel of a linear transformation is a subspace of the domain.

Short Answer

Expert verified

The given statement is true.

Step by step solution

01

kernel of linear transformation

Kernel of linear transformation T is a set of all vectors x such that T(x) = 0.

So, it is a subset of the domain.

02

Explanation for the above statement

Let x, y are two vectors from kernel and a, b are two scalars, then for a linear transformation T we have.

Tax+by=aTx+bty=0+0鈬�0

So, ax + by is in kernel, meaning that the kernel of linear transformation is subspace.

Hence, the given statement is true.

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