# 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.

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
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
2) surjective if $n\ge m=$ rank A
3) bijective if $m=n=$ rank A
Now injective but not surjective let us consider an example .
${A}_{3×2}=\left[\begin{array}{c}20\\ 03\\ 00\end{array}\right]$
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 $A\ne 3=$ dimension of the codomain
hence A is not surjective