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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Answer:
Step-by-step explanation:
so the question lets us know 3 things:
1) Sarah has a 27 ft pipe
2) she cuts 6 ft off
3) she cuts remaining pipe into 7 equal sections
what we don't know from the question is how big each of those 7 sections were. To form the equation we do this.
Since we know Sarah has 27 ft of pipe that would be our answer of the equation.
Sarah also removed 6 ft and the rest of the pipe she cut up into 7 small sections of equal length. since we don't know the length of the 7 smaller sections we will use the variable X to represent the length. this means that 6ft + 7x (X is the length of the pipes, and we multiply by 7 since there are 7 of them) must equal Sarah's total length of 27ft, therefore meaning our education would be
to solve for how long each pipe was, we need to solve for X by rearranging the equation as shown bellow.
The two equations are
and
the first equation can be solved for x to be
next you can substitute x in the second equation
Distribute 4 to everything in the parentheses
combine like terms:
subtract 28 from both sides of the equation
divide both sides by -1.5
plug this in to the original equation of x+y=7
subtract 4 from both sides.
Final Answer: they bought 3 adult tickets and 4 student tickets
Hope this helps!
and
the first equation can be solved for x to be
next you can substitute x in the second equation
Distribute 4 to everything in the parentheses
combine like terms:
subtract 28 from both sides of the equation
divide both sides by -1.5
plug this in to the original equation of x+y=7
subtract 4 from both sides.
Final Answer: they bought 3 adult tickets and 4 student tickets
Hope this helps!