Question

The kernel of a matrix transformation t(x)= ax is equal to the null space of matrix a. true or false

Answer 1

• It is true that the set of all u in V such that T(u)=0 is the kernel of a linear transformation, T, from a vector space V to a vector space W.
• As a result, the null space of A serves as the kernel of the matrix transformation T(x)=Ax. Vector space is the domain of a linear transformation.

What makes up a linear transformation's kernel?

The portion of the domain that is changed into the zero vector is known as the kernel (or null space) of a linear transformation.

Is kernel equivalent to empty space?

The linear subspace of the map's domain that is mapped to the zero vector is referred to in mathematics as the kernel of a linear map and is also known as the null space or null space.

Does kernel equate to basis?

• A vector space serves as the transformation's kernel (indeed, a subspace of the vector space on which the transformation acts).
• Since a basis cannot contain the zero vector, a basis for the kernel is never a vector space.

Learn more about null space

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