The kernel of a matrix transformation t(x)= ax is equal to the null space of matrix a. true or false
1 answer:
- 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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<u>ANSWER</u>
<u>EXPLANATION</u>
The given function is
We make the coefficient of unity by factoring
out of the last two terms to obtain;
We now add and subtract half the coefficient of multiplied by a factor of 6 to obtain;
We now factor 6 out of the last two terms to get;
The quadratic trinomial in the parenthesis is now a perfect square.
Hence the vertex form of the polynomial is