Find and describe an example of a matrix with each of the following properties. Briefly describe why the desired property is in the matrix you picked. If no such matrix exists, explain using a theorem studied. (a) A square matrix representing an injective but not a surjective transformation.

babeeb0oL 2020-12-15 Answered
Find and describe an example of a matrix with each of the following properties.
Briefly describe why the desired property is in the matrix you picked. If no such matrix exists, explain using a theorem studied.
(a) A square matrix representing an injective but not a surjective transformation.
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smallq9
Answered 2020-12-16 Author has 106 answers
Find and describe an example of a matrix with each of the following properties.
(a) A square matrix representing an injective but not a surjective transformation.
Given: we have a square matrix representing an injective transformation.
Explanation: in general for an m×n matrix A the rank
rank A=minm,n
matrix A will be
1) injective if mn= rank ADim(kerA)=0
2) surjective if nm= rank A
3) bijective if m=n= rank A
Now injective but not surjective let us consider an example .
A3×2=[200300]
here in the above matrix the number of rows are more than the number of column that is
3>2= rank A
since A is injective
but rank A3= dimension of the codomain
hence A is not surjective
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I. (2, 3)
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III, (m,n) interms of m and n
b)To show:
That under a half-turn with the origin as center, the image of a point (a, b) has coordinates (a, b).
c) To find:
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