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The Dimension Of The Image And Kernel Of A Linear Transformation

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Q2 The Dimension of The Image and Kernel of a Linear
Transformation
50 Points
Q2.1
25 Points
Consider at linear transformation 7(@) = A@, where A c R( *8, such that
dim( ker ( A) ) = 3.
What is dim ( im ( A) ) = ?
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Q2.2
25 Points
Consider at linear transformation 7(@) = BE, where B C IR*, such that
dim( im (B) ) = 3.
What is dim ( ker ( B) ) = ?
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Q2.3 Bonus Question (20 bonus points available)
0 Points
Consider at linear transformation T(@) = Ca, such that dim ( im (C) ) = 3, and
dim ( ker (C) ) = 4.
What can we say about
(1) the number of rows of C, and
(2) the number of columns of C ?Math