QUESTION 7 A linear transformationis A function f that satisfies f(ai + by -af)

Question

QUESTION 7 A linear transformationis A function f that satisfies f(ai + by -af) bf) OThe most common type of function O A function that maps lines to lines, but does not map the origin to itself A type of translation function QUESTION 8 Matrices are related to linear transformations in that Linear transformations are exactly the set of functions that can be represented by multiplying a vector by a matrix Linear transformations are the set of functions that act on matrices Matrices are the domain of linear transformations Linear transformations can be represented as vectors which act on matrices O QUESTION 9 The identity matrix is O The unique matrix 1 such that lx-x for all The only matrix which is tsown inverse O The only matrix that represents an affine transformation rather than a linear transformation Another name for the inverse of a given matrix

Explanation / Answer

Question 7:
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A Linear Transformation is:

Answer:-
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1.A function f that satisfy the f(ax+by)=af(x)+bf(y).

linear transformation is a mapping V ? W between two modules (including vector spaces) that preserves
the operations of addition and scalar multiplication.

For Example, A linear transformation between two vector spaces V and W is a map T:V->W

such that the following hold: T(v_1+v_2)=T(v_1)+T(v_2) for any vectors v_1 and v_2 in V

Question 8:-
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Answer:-
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1.Linear Transformation are exactly the set of functions that can be represented by multiplying a vector by a matrix.

Question 9:
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1.A Unique Matrix I such that Ix=x for all x.

The basic definition of identity is,
The n×n identity matrix, denoted In(start subscript, n, end subscript), is a matrix with n rows and n columns.
The entries on the diagonal from the upper left to the bottom right are all 1's, and all other entries are 0.

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