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Noone1982
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If L(x) = (x1, x2, 0)^t and L(x) = (x1, x1, x1)^t
What is the kernel and range?
What is the kernel and range?
Noone1982 said:If L(x) = (x1, x2, 0)^t and L(x) = (x1, x1, x1)^t
What is the kernel and range?
Noone1982 said:I need to do both. I know the kernel is basically setting to zero, but my book is awful on explaining stuff. I also know the range is basically solving for y and row reducing, but I am foggy on the presentation.
JasonRox said:Note: I have no idea what you mean by exponent t.
George Jones said:It means transpose. For example (5,2,3) is a row matrix (i.e., a 1x3 matrix) and (5,2,3)^t is a column matrix (i.e., a 3x1 matrix).
Regards,
George
HallsofIvy said:Then I'm surprised that you don't know that AT is a standard notation for transpose.
matt grime said:You can't guess that lower and upper case t in an expression x^t or x^T where x is a vector don't both obviously mean transpose?
A transformation is a mathematical operation that maps elements from one set to another. It can be represented by a function or matrix.
The kernel of a transformation, also known as the null space, is the set of all input values that result in an output of zero. In other words, it is the set of vectors that are mapped to the zero vector by the transformation.
To find the kernel of a transformation, you need to solve the system of equations that represents the transformation. This can be done by setting the transformation equal to the zero vector and solving for the input variables.
The range of a transformation is the set of all possible output values that the transformation can produce. In other words, it is the set of vectors that can be obtained by applying the transformation to the input vectors.
To find the range of a transformation, you can either determine the span of the columns of the transformation matrix or evaluate the transformation on a set of basis vectors. The resulting vectors will make up the range of the transformation.